Pub Date : 2026-02-01Epub Date: 2025-09-26DOI: 10.1016/j.nahs.2025.101647
Hoang Thi Duyen , Ky Quan Tran
This paper investigates -exponential stability – also known as exponential stability in the mean square – of neutral stochastic delay differential equations with impulsive perturbations. Our primary objective is to stabilize an impulsive-free system by appropriately designing impulsive controls. Unlike previous studies, we introduce new and verifiable criteria for -exponential stability. We further demonstrate that Euler–Maruyama-type approximations preserve -exponential stability provided that the step sizes are sufficiently small; explicit conditions on these step sizes are derived. Moreover, we detail the design of impulsive perturbations that achieve -exponential stabilization. Two examples are presented to validate the effectiveness of our criteria.
{"title":"L2-exponential stability and impulsive stabilization of neutral stochastic delay differential equations","authors":"Hoang Thi Duyen , Ky Quan Tran","doi":"10.1016/j.nahs.2025.101647","DOIUrl":"10.1016/j.nahs.2025.101647","url":null,"abstract":"<div><div>This paper investigates <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability – also known as exponential stability in the mean square – of neutral stochastic delay differential equations with impulsive perturbations. Our primary objective is to stabilize an impulsive-free system by appropriately designing impulsive controls. Unlike previous studies, we introduce new and verifiable criteria for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability. We further demonstrate that Euler–Maruyama-type approximations preserve <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stability provided that the step sizes are sufficiently small; explicit conditions on these step sizes are derived. Moreover, we detail the design of impulsive perturbations that achieve <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-exponential stabilization. Two examples are presented to validate the effectiveness of our criteria.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101647"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-11-14DOI: 10.1016/j.nahs.2025.101658
Mengqian Liang, Dan Ma, Jiaming Lu
This paper investigates the asynchronous data-driven control synthesis problem for continuous- and discrete-time switched linear systems, where exogenous disturbances and asynchronous behavior introduce significant challenges to control design. First, inspired by online data-driven techniques, a novel data representation of the systems is proposed under controller–subsystem asynchrony. Second, the data-dependent Lyapunov function combined with the merging average dwell time switching signal is constructed to establish sufficient conditions on robust practical exponential stabilization of the asynchronous switched control systems with disturbances. Furthermore, exponential stabilization is rigorously guaranteed in the disturbance-free case. Compared with the existing data-driven results, this paper eliminates the reliance on persistent excitation constraints, thereby substantially mitigating the conservatism in the robust stabilization criteria. Lastly, two numerical simulations are employed to verify the effectiveness of the proposed method.
{"title":"Data-driven asynchronous robust stabilization of switched linear systems with disturbances","authors":"Mengqian Liang, Dan Ma, Jiaming Lu","doi":"10.1016/j.nahs.2025.101658","DOIUrl":"10.1016/j.nahs.2025.101658","url":null,"abstract":"<div><div>This paper investigates the asynchronous data-driven control synthesis problem for continuous- and discrete-time switched linear systems, where exogenous disturbances and asynchronous behavior introduce significant challenges to control design. First, inspired by online data-driven techniques, a novel data representation of the systems is proposed under controller–subsystem asynchrony. Second, the data-dependent Lyapunov function combined with the merging average dwell time switching signal is constructed to establish sufficient conditions on robust practical exponential stabilization of the asynchronous switched control systems with disturbances. Furthermore, exponential stabilization is rigorously guaranteed in the disturbance-free case. Compared with the existing data-driven results, this paper eliminates the reliance on persistent excitation constraints, thereby substantially mitigating the conservatism in the robust stabilization criteria. Lastly, two numerical simulations are employed to verify the effectiveness of the proposed method.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101658"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-09-30DOI: 10.1016/j.nahs.2025.101644
Henk A.P. Blom
In MJLS literature the separation principle between filtering and control has been established in case the Markov mode switching process is fully observed, and the Euclidean state process is partially observed. In case the exact remains hidden, the separation principle has only been established under a linear filtering restriction. Since nonlinear filters can provide significant better estimates, the desire to extend the separation principle to MJLS with hidden is a long-standing challenge. The objective of this paper is to resolve this long-standing challenge in three steps. The first step is to transform the MJLS stochastic control problem into control under a quadratic performance criterion of a linear system driven by a martingale which is influenced by the control. The certainty equivalence (CE) condition known in literature applies to stochastic control of a linear system that is driven by a control independent martingale. Therefore, the second step is to relax this known CE condition such that it allows this control influence on the martingale. The third step is to prove that the relaxed CE condition is satisfied for the general MJLS control problem considered. The overall achievement is a CE control law for a partially observed MJLS, which assures the Separation Principle between filtering and control. The paper also shows that for the case that is fully observed and the exactremains hidden, that the novel CE control law differs significantly from the in literature well-developed Averaging MJLS control policy.
{"title":"Separation principle for stochastic control of continuous-time Markov jump linear systems under partial observations","authors":"Henk A.P. Blom","doi":"10.1016/j.nahs.2025.101644","DOIUrl":"10.1016/j.nahs.2025.101644","url":null,"abstract":"<div><div>In MJLS literature the separation principle between filtering and control has been established in case the Markov mode switching process <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span> is fully observed, and the Euclidean state process <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is partially observed. In case the exact <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>remains hidden, the separation principle has only been established under a linear filtering restriction. Since nonlinear filters can provide significant better estimates, the desire to extend the separation principle to MJLS with hidden <span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is a long-standing challenge. The objective of this paper is to resolve this long-standing challenge in three steps. The first step is to transform the MJLS stochastic control problem into control under a quadratic performance criterion of a linear system driven by a martingale which is influenced by the control. The certainty equivalence (CE) condition known in literature applies to stochastic control of a linear system that is driven by a control independent martingale. Therefore, the second step is to relax this known CE condition such that it allows this control influence on the martingale. The third step is to prove that the relaxed CE condition is satisfied for the general MJLS control problem considered. The overall achievement is a CE control law for a partially observed MJLS, which assures the Separation Principle between filtering and control. The paper also shows that for the case that <span><math><mrow><mo>{</mo><msub><mi>x</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>is fully observed and the exact<span><math><mrow><mo>{</mo><msub><mi>θ</mi><mi>t</mi></msub><mo>}</mo></mrow></math></span>remains hidden, that the novel CE control law differs significantly from the in literature well-developed Averaging MJLS control policy.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101644"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a robust sampled controller design for trajectory tracking in unicycle mobile robots subject to state, input, and communication constraints, as well as external disturbances such as wheel slipping. The proposed approach integrates two control strategies: an aperiodic control law based on an event-triggered mechanism and a periodic control law using a constant sampled state-feedback controller. The event-triggered control employs the attractive ellipsoid method and the barrier Lyapunov function to ensure performance within a defined safe set, where state constraints are preserved, and a switching set determines the active control strategy. The periodic sampled control considers the maximum sampling time required to achieve trajectory tracking while minimizing bandwidth usage. This strategy guarantees input-to-state stability of the tracking error dynamics against multiplicative external disturbances. Additionally, a straightforward method using linear matrix inequalities is provided to compute the controller gains. Experimental results validate the effectiveness of the proposed robust control approach.
{"title":"An event-triggered robust sampled tracking controller for communication-state-input constrained perturbed unicycle mobile robots","authors":"Ariana Gutiérrez , Héctor Ríos , Manuel Mera , Denis Efimov , Rosane Ushirobira","doi":"10.1016/j.nahs.2025.101657","DOIUrl":"10.1016/j.nahs.2025.101657","url":null,"abstract":"<div><div>This paper presents a robust sampled controller design for trajectory tracking in unicycle mobile robots subject to state, input, and communication constraints, as well as external disturbances such as wheel slipping. The proposed approach integrates two control strategies: an aperiodic control law based on an event-triggered mechanism and a periodic control law using a constant sampled state-feedback controller. The event-triggered control employs the attractive ellipsoid method and the barrier Lyapunov function to ensure performance within a defined safe set, where state constraints are preserved, and a switching set determines the active control strategy. The periodic sampled control considers the maximum sampling time required to achieve trajectory tracking while minimizing bandwidth usage. This strategy guarantees input-to-state stability of the tracking error dynamics against multiplicative external disturbances. Additionally, a straightforward method using linear matrix inequalities is provided to compute the controller gains. Experimental results validate the effectiveness of the proposed robust control approach.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101657"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-10-11DOI: 10.1016/j.nahs.2025.101651
Roberto M. Fuentes , Gabriela W. Gabriel , André M. de Oliveira , Jonathan M. Palma
This paper studies the reference-tracking control problem for uncertain sampled-data systems with partial observation of the states. We show that, by robustly stabilizing the closed-loop system, the proposed digital controller ensures that the controlled output tracks constant set points. Moreover, new design conditions given in terms of Differential Linear Matrix Inequalities are presented for obtaining controllers with partial and complete measurements of the states. The design conditions are illustrated by numerical examples.
{"title":"Constant reference tracking control for uncertain linear sampled-data systems","authors":"Roberto M. Fuentes , Gabriela W. Gabriel , André M. de Oliveira , Jonathan M. Palma","doi":"10.1016/j.nahs.2025.101651","DOIUrl":"10.1016/j.nahs.2025.101651","url":null,"abstract":"<div><div>This paper studies the reference-tracking control problem for uncertain sampled-data systems with partial observation of the states. We show that, by robustly stabilizing the closed-loop system, the proposed digital controller ensures that the controlled output tracks constant set points. Moreover, new design conditions given in terms of Differential Linear Matrix Inequalities are presented for obtaining controllers with partial and complete measurements of the states. The design conditions are illustrated by numerical examples.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101651"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-09-18DOI: 10.1016/j.nahs.2025.101642
Xiaoyun Wei , Xingwen Liu , Jun Yang , Tingjin Liu
This paper focuses on exponential stability analysis for discrete-time almost periodic piecewise nonlinear systems (APPNSs) with uncertain dwell time of subsystems. A discrete-time APPNS has a fundamental period, during which a finite number of subsystems that constitute the system are cyclically activated. Such systems can be modeled as switched systems with cyclically switching signals. With the assumption that the vector field of each subsystem of discrete-time APPNSs is continuously differentiable, a Lyapunov theorem is presented first to verify the exponential stability of discrete-time APPNSs. Then, a linearization method is employed and a mixed-mode time-varying homogeneous Lyapunov function is constructed to derive specific stability conditions expressed by linear matrix inequalities (LMIs). Note that this condition can verify the exponential stability of the considered nonlinear systems, as well as that of the corresponding linearized systems. Furthermore, the linearization method used here can be applied to general switched systems.
{"title":"Exponential stability analysis of discrete-time almost periodic piecewise nonlinear systems","authors":"Xiaoyun Wei , Xingwen Liu , Jun Yang , Tingjin Liu","doi":"10.1016/j.nahs.2025.101642","DOIUrl":"10.1016/j.nahs.2025.101642","url":null,"abstract":"<div><div>This paper focuses on exponential stability analysis for discrete-time almost periodic piecewise nonlinear systems (APPNSs) with uncertain dwell time of subsystems. A discrete-time APPNS has a fundamental period, during which a finite number of subsystems that constitute the system are cyclically activated. Such systems can be modeled as switched systems with cyclically switching signals. With the assumption that the vector field of each subsystem of discrete-time APPNSs is continuously differentiable, a Lyapunov theorem is presented first to verify the exponential stability of discrete-time APPNSs. Then, a linearization method is employed and a mixed-mode time-varying homogeneous Lyapunov function is constructed to derive specific stability conditions expressed by linear matrix inequalities (LMIs). Note that this condition can verify the exponential stability of the considered nonlinear systems, as well as that of the corresponding linearized systems. Furthermore, the linearization method used here can be applied to general switched systems.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101642"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-10-17DOI: 10.1016/j.nahs.2025.101653
Yanan Pan , Shihua Fu , Jianjun Wang , Weihai Zhang
This paper studies the optimal output regulation of Boolean control networks (BCNs), the main objective of which is to design a state feedback control such that the tracking error of each state trajectory in the system is minimized. Firstly, the definition of the solvability for the output regulation within admissible tracking error is given, and some necessary and sufficient conditions to determine the solvability of the output regulation problem within admissible tracking error are obtained. Secondly, the optimal trajectory of each state is provided when the outputs of the BCN cannot completely track the time-varying reference signals, and a control design algorithm that minimizes the tracking error of the system is introduced. Finally, two examples are given to verify the validity of our new findings.
{"title":"Optimal output regulation of Boolean control networks","authors":"Yanan Pan , Shihua Fu , Jianjun Wang , Weihai Zhang","doi":"10.1016/j.nahs.2025.101653","DOIUrl":"10.1016/j.nahs.2025.101653","url":null,"abstract":"<div><div>This paper studies the optimal output regulation of Boolean control networks (BCNs), the main objective of which is to design a state feedback control such that the tracking error of each state trajectory in the system is minimized. Firstly, the definition of the solvability for the output regulation within admissible tracking error is given, and some necessary and sufficient conditions to determine the solvability of the output regulation problem within admissible tracking error are obtained. Secondly, the optimal trajectory of each state is provided when the outputs of the BCN cannot completely track the time-varying reference signals, and a control design algorithm that minimizes the tracking error of the system is introduced. Finally, two examples are given to verify the validity of our new findings.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101653"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-10-16DOI: 10.1016/j.nahs.2025.101650
Agustín G. Yabo , Nicolas Augier
In this paper, we investigate optimal state transfers for a generic class of piecewise-linear models widely used to qualitatively describe gene-regulatory networks. Motivated by the main practical drawbacks of artificially regulating gene expression through chemical inducers, the optimality of the transitions is defined as the convex combination of the total time and the cost of the control. Solutions are studied through a Hybrid Pontryagin’s Maximum Principle approach, which allows to characterize the optimal trajectories and control for the general formulation of the problem. Then, we focus on two practical examples of two-dimensional regulatory networks: the bistable switch, for which the objective is to induce optimal transitions between its two stable steady states, and the damped genetic oscillator, where the goal is to induce sustained oscillatory behaviors. The resulting optimal control strategies can be expressed in state feedback form, involving both bang arcs and inactive control periods, and are shown to slide over certain separatrices of the uncontrolled system that characterize the boundaries of the admissibility set.
{"title":"On L1 and time-optimal state transitions in piecewise linear models of gene-regulatory networks","authors":"Agustín G. Yabo , Nicolas Augier","doi":"10.1016/j.nahs.2025.101650","DOIUrl":"10.1016/j.nahs.2025.101650","url":null,"abstract":"<div><div>In this paper, we investigate optimal state transfers for a generic class of piecewise-linear models widely used to qualitatively describe gene-regulatory networks. Motivated by the main practical drawbacks of artificially regulating gene expression through chemical inducers, the optimality of the transitions is defined as the convex combination of the total time and the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> cost of the control. Solutions are studied through a Hybrid Pontryagin’s Maximum Principle approach, which allows to characterize the optimal trajectories and control for the general formulation of the problem. Then, we focus on two practical examples of two-dimensional regulatory networks: the bistable switch, for which the objective is to induce optimal transitions between its two stable steady states, and the damped genetic oscillator, where the goal is to induce sustained oscillatory behaviors. The resulting optimal control strategies can be expressed in state feedback form, involving both bang arcs and inactive control periods, and are shown to slide over certain separatrices of the uncontrolled system that characterize the boundaries of the admissibility set.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101650"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-10-16DOI: 10.1016/j.nahs.2025.101649
Hussein Sibai , Enrique Mallada
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be (-)recurrent if every trajectory that starts in the set returns to it (within at most units of time). The recurrence entropy of a control system quantifies the complexity of making a set -recurrent measured by the average rate of growth, as time increases, of the number of control signals required to achieve this goal. Our analysis reveals that, compared to invariance, recurrence is quantitatively less complex, meaning that the recurrence entropy of a set is no larger than, and often strictly smaller than, the invariance entropy. We provide upper and lower bounds on recurrence entropy and show that they converge to the bounds on invariance entropy as decreases to zero. Further, our results show that recurrence entropy lower bounds the minimum data rate between the sensor and controller required for achieving recurrence. We present an algorithm according to which the sensor can send state estimates to the controller over a limited-bandwidth channel to achieve recurrence asymptotically at an exponential rate. Finally, we show that, under mild stricter conditions on the set and dynamics, the control signals that enforce the -recurrence of a set can be generated by a finite alphabet of control signals of durations of at most units of time, which allows us to store them for quick online execution.
{"title":"Recurrence of nonlinear control systems: Entropy, bit rates, and finite alphabet controllers","authors":"Hussein Sibai , Enrique Mallada","doi":"10.1016/j.nahs.2025.101649","DOIUrl":"10.1016/j.nahs.2025.101649","url":null,"abstract":"<div><div>In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be (<span><math><mi>τ</mi></math></span>-)recurrent if every trajectory that starts in the set returns to it (within at most <span><math><mi>τ</mi></math></span> units of time). The recurrence entropy of a control system quantifies the complexity of making a set <span><math><mi>τ</mi></math></span>-recurrent measured by the average rate of growth, as time increases, of the number of control signals required to achieve this goal. Our analysis reveals that, compared to invariance, recurrence is quantitatively less complex, meaning that the recurrence entropy of a set is no larger than, and often strictly smaller than, the invariance entropy. We provide upper and lower bounds on recurrence entropy and show that they converge to the bounds on invariance entropy as <span><math><mi>τ</mi></math></span> decreases to zero. Further, our results show that recurrence entropy lower bounds the minimum data rate between the sensor and controller required for achieving recurrence. We present an algorithm according to which the sensor can send state estimates to the controller over a limited-bandwidth channel to achieve recurrence asymptotically at an exponential rate. Finally, we show that, under mild stricter conditions on the set and dynamics, the control signals that enforce the <span><math><mi>τ</mi></math></span>-recurrence of a set can be generated by a finite alphabet of control signals of durations of at most <span><math><mi>τ</mi></math></span> units of time, which allows us to store them for quick online execution.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101649"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.nahs.2025.101655
Jianrui Li, Jinghai Shao
The recurrent property of diffusion processes with regime-switching is quite complicated, which could be transient even when it is recurrent at every fixed environment. This work provides explicit criteria in terms of the coefficients of diffusion processes such that the studied processes are recurrent or transient under arbitrary switching rates. The obtained criteria are in the integral form, which are particularly effective for the regime-switching processes with coefficients vibrating periodically. Examples are constructed to illustrate the applications of these criteria.
{"title":"Explicit criteria for recurrence of Markovian regime-switching diffusion processes under arbitrary switching rates","authors":"Jianrui Li, Jinghai Shao","doi":"10.1016/j.nahs.2025.101655","DOIUrl":"10.1016/j.nahs.2025.101655","url":null,"abstract":"<div><div>The recurrent property of diffusion processes with regime-switching is quite complicated, which could be transient even when it is recurrent at every fixed environment. This work provides explicit criteria in terms of the coefficients of diffusion processes such that the studied processes are recurrent or transient under arbitrary switching rates. The obtained criteria are in the integral form, which are particularly effective for the regime-switching processes with coefficients vibrating periodically. Examples are constructed to illustrate the applications of these criteria.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101655"},"PeriodicalIF":3.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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