Pub Date : 2026-01-28DOI: 10.1016/j.sysconle.2026.106363
Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat
This paper solves the problem of output feedback stabilization for a cascade of heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar output being either a distributed or a pointwise in-domain measurement done on the last equation of the cascade. Two different configurations are studied in details. The first one consists of a cascade of heat equations with totally disconnected spectra. The second one consists of a cascade of identical heat equations, inducing eigenvalues of multiplicity . In both cases, the problem is solved thanks to a spectral analysis and a study of the modal controllability and observability properties. The key point is that the generalized eigenvectors form a Riesz basis of the state space. The stabilization property is established in and norms.
{"title":"Boundary output feedback stabilization of a cascade of N heat equations","authors":"Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat","doi":"10.1016/j.sysconle.2026.106363","DOIUrl":"10.1016/j.sysconle.2026.106363","url":null,"abstract":"<div><div>This paper solves the problem of output feedback stabilization for a cascade of <span><math><mi>N</mi></math></span> heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar output being either a distributed or a pointwise in-domain measurement done on the last equation of the cascade. Two different configurations are studied in details. The first one consists of a cascade of <span><math><mi>N</mi></math></span> heat equations with totally disconnected spectra. The second one consists of a cascade of <span><math><mi>N</mi></math></span> identical heat equations, inducing eigenvalues of multiplicity <span><math><mi>N</mi></math></span>. In both cases, the problem is solved thanks to a spectral analysis and a study of the modal controllability and observability properties. The key point is that the generalized eigenvectors form a Riesz basis of the state space. The stabilization property is established in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"210 ","pages":"Article 106363"},"PeriodicalIF":2.5,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-28DOI: 10.1016/j.sysconle.2026.106362
Xin Chen
Uncertainty theory provides a powerful framework for addressing optimal control problems under indeterminate conditions. In this paper, we focus on the theoretical analysis of optimal control for uncertain singular systems using the -pessimistic value criterion within the uncertainty theory framework. We propose a novel optimal control problem and introduce a theoretical method for deriving the optimal solution. To solve this problem effectively, we establish the equivalence between the optimal control problem of uncertain singular systems and that of standard uncertain systems through algebraic transformation methods. We then derive a recurrence equation based on the properties of the -pessimistic value and dynamic programming principle. Under the -pessimistic criterion, we consider two classes of uncertain singular optimal control problems. For each class, explicit analytical solutions for the optimal controls and their corresponding values are acquired through the recurrence equation. Finally, numerical examples are presented to demonstrate the effectiveness of the obtained results.
{"title":"Optimal control of uncertain singular systems based on the α-pessimistic value","authors":"Xin Chen","doi":"10.1016/j.sysconle.2026.106362","DOIUrl":"10.1016/j.sysconle.2026.106362","url":null,"abstract":"<div><div>Uncertainty theory provides a powerful framework for addressing optimal control problems under indeterminate conditions. In this paper, we focus on the theoretical analysis of optimal control for uncertain singular systems using the <span><math><mi>α</mi></math></span>-pessimistic value criterion within the uncertainty theory framework. We propose a novel optimal control problem and introduce a theoretical method for deriving the optimal solution. To solve this problem effectively, we establish the equivalence between the optimal control problem of uncertain singular systems and that of standard uncertain systems through algebraic transformation methods. We then derive a recurrence equation based on the properties of the <span><math><mi>α</mi></math></span>-pessimistic value and dynamic programming principle. Under the <span><math><mi>α</mi></math></span>-pessimistic criterion, we consider two classes of uncertain singular optimal control problems. For each class, explicit analytical solutions for the optimal controls and their corresponding values are acquired through the recurrence equation. Finally, numerical examples are presented to demonstrate the effectiveness of the obtained results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"210 ","pages":"Article 106362"},"PeriodicalIF":2.5,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-24DOI: 10.1016/j.sysconle.2026.106364
Jiayao Zhang, Zhi Li
In this paper, we investigate the containment control for high-order systems subject to both convex state constraints and nonconvex input constraints under switching topologies. The primary challenge lies in addressing the complex nonlinearities arising from these diverse constraints and the intricate couplings in high-order system states. To address the constrained containment, we propose a nonlinear distributed control protocol that ensures all followers converge to the convex hull formed by stationary leaders, while guaranteeing that both state and input trajectories remain within their respective constrained sets. By introducing scaling factors and projection errors, the original constrained high-order system is transformed into an equivalent unconstrained system. Subsequently, a Lyapunov function is constructed based on the maximum distance between each follower and the convex hull. Using convex analysis together with properties of the projection operator, we demonstrate that this Lyapunov function is monotonically nonincreasing, which effectively eliminates the errors introduced by the convex constraints. Furthermore, by incorporating the lower bound of the scaling factor and Lyapunov stability, it can be proven that all followers converge to a convex hull, provided that there exists at least one directed path to one of the leaders for all followers in the union of topologies. A numerical simulation confirms the effectiveness of the proposed theorem.
{"title":"Containment control for high-order systems with convex state and nonconvex input constraints under switching topologies","authors":"Jiayao Zhang, Zhi Li","doi":"10.1016/j.sysconle.2026.106364","DOIUrl":"10.1016/j.sysconle.2026.106364","url":null,"abstract":"<div><div>In this paper, we investigate the containment control for high-order systems subject to both convex state constraints and nonconvex input constraints under switching topologies. The primary challenge lies in addressing the complex nonlinearities arising from these diverse constraints and the intricate couplings in high-order system states. To address the constrained containment, we propose a nonlinear distributed control protocol that ensures all followers converge to the convex hull formed by stationary leaders, while guaranteeing that both state and input trajectories remain within their respective constrained sets. By introducing scaling factors and projection errors, the original constrained high-order system is transformed into an equivalent unconstrained system. Subsequently, a Lyapunov function is constructed based on the maximum distance between each follower and the convex hull. Using convex analysis together with properties of the projection operator, we demonstrate that this Lyapunov function is monotonically nonincreasing, which effectively eliminates the errors introduced by the convex constraints. Furthermore, by incorporating the lower bound of the scaling factor and Lyapunov stability, it can be proven that all followers converge to a convex hull, provided that there exists at least one directed path to one of the leaders for all followers in the union of topologies. A numerical simulation confirms the effectiveness of the proposed theorem.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106364"},"PeriodicalIF":2.5,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-24DOI: 10.1016/j.sysconle.2026.106365
Tian Zhang , Hong-Xiang Hu , Xiaoling Wang , Yun Chen , Tingwen Huang
This paper addresses the exponential stabilization of highly nonlinear stochastic coupled systems with pantograph delay under aperiodically intermittent control. Two main obstacles are overcome. First, the unbounded pantograph delay coupled with high-order nonlinearities invalidates conventional Halanay-type inequalities for intermittent control analysis. We establish a novel Halanay-type inequality to resolve this. Second, in the stochastic setting, direct use of this inequality is hindered by Jensen’s inequality (which, for , gives ), preventing the interchange of expectation and nonlinear powers. To bridge this gap, we construct an auxiliary Lyapunov functional. This functional, when differentiated by Leibniz’s rule, cancels key pantograph delay terms and enables rigorous application of the new inequality. Integrating this framework with Itô’s formula and graph theory, we derive two verifiable exponential stability criteria: a Lyapunov-type and a coefficient-type criterion. The effectiveness of the proposed strategy is validated through a modified stochastic coupled Fitzhugh–Nagumo model and numerical simulations.
{"title":"Stabilization of highly nonlinear stochastic coupled systems with pantograph delay via completely aperiodically intermittent control","authors":"Tian Zhang , Hong-Xiang Hu , Xiaoling Wang , Yun Chen , Tingwen Huang","doi":"10.1016/j.sysconle.2026.106365","DOIUrl":"10.1016/j.sysconle.2026.106365","url":null,"abstract":"<div><div>This paper addresses the exponential stabilization of highly nonlinear stochastic coupled systems with pantograph delay under aperiodically intermittent control. Two main obstacles are overcome. First, the unbounded pantograph delay coupled with high-order nonlinearities invalidates conventional Halanay-type inequalities for intermittent control analysis. We establish a novel Halanay-type inequality to resolve this. Second, in the stochastic setting, direct use of this inequality is hindered by Jensen’s inequality (which, for <span><math><mrow><mi>α</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, gives <span><math><mrow><mi>E</mi><msup><mrow><mi>W</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>≥</mo><msup><mrow><mrow><mo>[</mo><mi>E</mi><mi>W</mi><mo>]</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span>), preventing the interchange of expectation and nonlinear powers. To bridge this gap, we construct an auxiliary Lyapunov functional. This functional, when differentiated by Leibniz’s rule, cancels key pantograph delay terms and enables rigorous application of the new inequality. Integrating this framework with Itô’s formula and graph theory, we derive two verifiable exponential stability criteria: a Lyapunov-type and a coefficient-type criterion. The effectiveness of the proposed strategy is validated through a modified stochastic coupled Fitzhugh–Nagumo model and numerical simulations.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106365"},"PeriodicalIF":2.5,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.sysconle.2026.106357
Yonghan Li , Chenyu Wu , Taoran Wu , Shijie Wang , Bai Xue
In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is a converse theorem: we prove that a continuously differentiable, time-dependent barrier certificate exists if and only if the system is safe over the finite-time horizon. The existence problem is explored by finding a continuously differentiable approximation of a unique Lipschitz viscosity solution to a Hamilton–Jacobi equation.
{"title":"Converse barrier certificates for finite-time safety verification of continuous-time perturbed deterministic systems","authors":"Yonghan Li , Chenyu Wu , Taoran Wu , Shijie Wang , Bai Xue","doi":"10.1016/j.sysconle.2026.106357","DOIUrl":"10.1016/j.sysconle.2026.106357","url":null,"abstract":"<div><div>In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is a converse theorem: we prove that a continuously differentiable, time-dependent barrier certificate exists if and only if the system is safe over the finite-time horizon. The existence problem is explored by finding a continuously differentiable approximation of a unique Lipschitz viscosity solution to a Hamilton–Jacobi equation.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106357"},"PeriodicalIF":2.5,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.sysconle.2026.106351
Xin Zhang, Zongyuan Huang
By using the generalized continuity method in the mean-field framework, we obtain the existence and uniqueness results of fully coupled mean-field forward–backward stochastic differential equations with an arbitrarily large time duration, in the sense of th () power integrability. The coefficients of the equations depend not only on the solution processes, but also on their expectations. Furthermore, we establish the comparison theorems for coupled mean-field forward–backward stochastic differential equations in one-dimension and multi-dimension by the probabilistic method and duality technique in the mean-field context. Some stochastic Hamiltonian systems arising in stochastic optimal control systems and mathematical finance can be treated within our framework.
{"title":"Well-posedness and comparison theorems of coupled mean-field forward–backward stochastic differential equations","authors":"Xin Zhang, Zongyuan Huang","doi":"10.1016/j.sysconle.2026.106351","DOIUrl":"10.1016/j.sysconle.2026.106351","url":null,"abstract":"<div><div>By using the generalized continuity method in the mean-field framework, we obtain the existence and uniqueness results of fully coupled mean-field forward–backward stochastic differential equations with an arbitrarily large time duration, in the sense of <span><math><mi>p</mi></math></span>th (<span><math><mrow><mi>p</mi><mo>≥</mo><mn>2</mn></mrow></math></span>) power integrability. The coefficients of the equations depend not only on the solution processes, but also on their expectations. Furthermore, we establish the comparison theorems for coupled mean-field forward–backward stochastic differential equations in one-dimension and multi-dimension by the probabilistic method and duality technique in the mean-field context. Some stochastic Hamiltonian systems arising in stochastic optimal control systems and mathematical finance can be treated within our framework.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106351"},"PeriodicalIF":2.5,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.sysconle.2025.106338
Ramen Ghosh
We study the ergodic control of stochastic hybrid systems by shaping their invariant distribution. Given a regime-switching diffusion with feedback, we pose long-run optimal control with convex constraints on the stationary occupation measure to encode safety, fairness, and coverage requirements. Our analysis establishes (i) verifiable conditions ensuring existence and uniqueness of an invariant measure under controlled switching; (ii) a variational formulation on with a Wasserstein–KKT optimality system that links dual multipliers to sensitivities of stationary constraints; and (iii) sharp bifurcations of the optimal invariant law and dual variables as constraint thresholds, switching rates, or noise intensities vary, revealing phase-transition phenomena predicted by large-deviation heuristics. We further develop a simulation-based primal–dual synthesis method that estimates stationary occupancies from long trajectories and provably converges to a KKT point under standard step–size and convexity assumptions. Case studies — marine navigation in adversarial seas, battery–inverter management under stochastic load, and safety–enveloped medical device scheduling — demonstrate distributional guarantees unattainable by transient or average-cost criteria. The results provide a principled route to safe and interpretable autonomy in hybrid systems, with certificates phrased directly at the level of invariant laws.
{"title":"Stochastic ergodic control in hybrid systems: A framework for safe autonomy in adversarial environments","authors":"Ramen Ghosh","doi":"10.1016/j.sysconle.2025.106338","DOIUrl":"10.1016/j.sysconle.2025.106338","url":null,"abstract":"<div><div>We study the ergodic control of stochastic hybrid systems by <em>shaping their invariant distribution</em>. Given a regime-switching diffusion with feedback, we pose long-run optimal control with <em>convex constraints on the stationary occupation measure</em> to encode safety, fairness, and coverage requirements. Our analysis establishes (i) verifiable conditions ensuring existence and uniqueness of an invariant measure under controlled switching; (ii) a variational formulation on <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> with a <em>Wasserstein–KKT</em> optimality system that links dual multipliers to sensitivities of stationary constraints; and (iii) <em>sharp bifurcations</em> of the optimal invariant law and dual variables as constraint thresholds, switching rates, or noise intensities vary, revealing phase-transition phenomena predicted by large-deviation heuristics. We further develop a simulation-based primal–dual synthesis method that estimates stationary occupancies from long trajectories and provably converges to a KKT point under standard step–size and convexity assumptions. Case studies — marine navigation in adversarial seas, battery–inverter management under stochastic load, and safety–enveloped medical device scheduling — demonstrate distributional guarantees unattainable by transient or average-cost criteria. The results provide a principled route to safe and interpretable autonomy in hybrid systems, with certificates phrased directly at the level of invariant laws.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106338"},"PeriodicalIF":2.5,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.sysconle.2026.106359
Xiaopeng Shi , Chuanhou Gao , Denis Dochain , Yuzhen Fan
Embedding efficient calculation instructions into biochemical systems has always been a research focus in synthetic biology. Amongst this, the main challenge is how to overcome the contradiction between the parallel occurrence of biochemical reactions and the ordinal implementation of calculation instructions. In response to this challenge, the current work presents a new 4-dimensional biochemical oscillator model based on the relaxation oscillation to generate a pair of symmetric clock signals for dual-module regulation tasks through chemical reaction networks. The pair of symmetric clock signals separately act as a catalyst to participate the corresponding reaction modular of performing calculation, and control their on/off switch if the concentration of the clock signal is nonzero. The detailed discussions are subsequently made on the important effect of the oscillator parameters on controlling the period and the occurrence order of clock signals. Further, the oscillator is applied to control the iteration calculation, along with which a termination strategy is proposed to jump out of the loop.
{"title":"Biochemical relaxation oscillator designed to control molecular computation","authors":"Xiaopeng Shi , Chuanhou Gao , Denis Dochain , Yuzhen Fan","doi":"10.1016/j.sysconle.2026.106359","DOIUrl":"10.1016/j.sysconle.2026.106359","url":null,"abstract":"<div><div>Embedding efficient calculation instructions into biochemical systems has always been a research focus in synthetic biology. Amongst this, the main challenge is how to overcome the contradiction between the parallel occurrence of biochemical reactions and the ordinal implementation of calculation instructions. In response to this challenge, the current work presents a new 4-dimensional biochemical oscillator model based on the relaxation oscillation to generate a pair of symmetric clock signals for dual-module regulation tasks through chemical reaction networks. The pair of symmetric clock signals separately act as a catalyst to participate the corresponding reaction modular of performing calculation, and control their on/off switch if the concentration of the clock signal is nonzero. The detailed discussions are subsequently made on the important effect of the oscillator parameters on controlling the period and the occurrence order of clock signals. Further, the oscillator is applied to control the iteration calculation, along with which a termination strategy is proposed to jump out of the loop.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106359"},"PeriodicalIF":2.5,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the problem of state estimation using a network of distributed observers for continuous-time linear descriptor systems. Remarkably, the network of state observers is obtained as state-space systems even though the underlying distributed system is a linear descriptor system. We derive sufficient conditions in terms of the underlying system matrices for the existence of this network of state observers. The derived sufficient conditions consist of solving a linear matrix inequality, making the design easily implementable. Moreover, we introduce the notion of joint detectability of the original system and show that it is necessary for the design of the distributed observers. Finally, the developed theory is illustrated with a numerical example.
{"title":"Distributed state estimation of linear descriptor systems","authors":"Juhi Jaiswal , Vikas Kumar Mishra , Raghunathan Rengaswamy , Naim Bajcinca","doi":"10.1016/j.sysconle.2026.106360","DOIUrl":"10.1016/j.sysconle.2026.106360","url":null,"abstract":"<div><div>In this paper, we study the problem of state estimation using a network of distributed observers for continuous-time linear descriptor systems. Remarkably, the network of state observers is obtained as state-space systems even though the underlying distributed system is a linear descriptor system. We derive sufficient conditions in terms of the underlying system matrices for the existence of this network of state observers. The derived sufficient conditions consist of solving a linear matrix inequality, making the design easily implementable. Moreover, we introduce the notion of joint detectability of the original system and show that it is necessary for the design of the distributed observers. Finally, the developed theory is illustrated with a numerical example.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106360"},"PeriodicalIF":2.5,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.sysconle.2026.106361
Dong-Hui Yang , Bao-Zhu Guo
This paper draws inspiration from Araruna et al. (2019), wherein the null controllability of a two-dimensional degenerate parabolic partial differential equation was demonstrated by restricting the control domain to lie near the degenerate boundary. In contrast, this study relaxes this constraint, allowing the control domain to be any small nonempty open subset. The approach adopted here is the Lebeau–Robbiano spectral inequality. Firstly, we define the solution space and discuss the properties of the solution. Additionally, the method of separation of variables is incorporated. The controllability, contingent upon uniform observability, is subsequently established. Finally, as an illustrative application, we extend this methodology to a different higher-dimensional example to highlight the limitations inherent in this approach.
本文的灵感来自Araruna et al.(2019)，其中通过将控制域限制在退化边界附近来证明二维退化抛物型偏微分方程的零可控性。相反，本研究放宽了这一约束，允许控制域是任何小的非空开放子集。这里采用的方法是Lebeau-Robbiano谱不等式。首先，我们定义了解空间并讨论了解的性质。此外，还采用了分离变量的方法。随后建立了以均匀可观测性为条件的可控性。最后，作为一个说明性应用程序，我们将该方法扩展到一个不同的高维示例，以突出该方法固有的局限性。
{"title":"Null controllability of a class of degenerate parabolic equations subject to Dirichlet boundary conditions","authors":"Dong-Hui Yang , Bao-Zhu Guo","doi":"10.1016/j.sysconle.2026.106361","DOIUrl":"10.1016/j.sysconle.2026.106361","url":null,"abstract":"<div><div>This paper draws inspiration from Araruna et al. (2019), wherein the null controllability of a two-dimensional degenerate parabolic partial differential equation was demonstrated by restricting the control domain to lie near the degenerate boundary. In contrast, this study relaxes this constraint, allowing the control domain to be any small nonempty open subset. The approach adopted here is the Lebeau–Robbiano spectral inequality. Firstly, we define the solution space and discuss the properties of the solution. Additionally, the method of separation of variables is incorporated. The controllability, contingent upon uniform observability, is subsequently established. Finally, as an illustrative application, we extend this methodology to a different higher-dimensional example to highlight the limitations inherent in this approach.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106361"},"PeriodicalIF":2.5,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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