Pub Date : 2026-05-01Epub Date: 2026-01-24DOI: 10.1016/j.nahs.2026.101682
Bernard Brogliato , Aneel Tanwani
This article is largely concerned with generic interconnections of a class of passive nonsmooth nonlinear dynamical systems, namely linear cone complementarity systems (LCCS). We stipulate that each subsystem admits a positive definite storage function that characterizes the passivity of an underlying nonsmooth mapping. We provide algebraic criteria in terms of these individual storage functions to find the storage function which guarantees passivity of the overall interconnected system. State jumps in the interconnections are studied in detail. Examples from dynamic feedback control, switching DAEs, interconnected sweeping processes, and nonsmooth circuits are included as an illustration of the theoretical developments.
{"title":"Passivity preservation in interconnections of linear cone complementarity systems with state jumps","authors":"Bernard Brogliato , Aneel Tanwani","doi":"10.1016/j.nahs.2026.101682","DOIUrl":"10.1016/j.nahs.2026.101682","url":null,"abstract":"<div><div>This article is largely concerned with generic interconnections of a class of passive nonsmooth nonlinear dynamical systems, namely linear cone complementarity systems (LCCS). We stipulate that each subsystem admits a positive definite storage function that characterizes the passivity of an underlying nonsmooth mapping. We provide algebraic criteria in terms of these individual storage functions to find the storage function which guarantees passivity of the overall interconnected system. State jumps in the interconnections are studied in detail. Examples from dynamic feedback control, switching DAEs, interconnected sweeping processes, and nonsmooth circuits are included as an illustration of the theoretical developments.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101682"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037579","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 : 2026-05-01Epub Date: 2026-01-25DOI: 10.1016/j.nahs.2026.101680
Rajab Aghamov , Christel Baier , Toghrul Karimov , Joël Ouaknine , Jakob Piribauer
In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly applied to an initial vector yielding a sequence of vectors called the orbit of the system. A weight function assigning weights to the points in the orbit can be used to model quantitative aspects, such as resource consumption, of a system modelled by an LDS. This paper addresses the problems of how to compute the mean payoff, the total accumulated weight, and the discounted accumulated weight of the orbit under continuous weight functions as well as polynomial weight functions as a special case. Additionally, weight functions that are definable in an o-minimal extension of the theory of the reals with exponentiation, which can be shown to be piecewise continuous, are considered. In particular, good ergodic properties of o-minimal weight functions, instrumental to the computation of the mean payoff, are established. Besides general LDSs, the special cases of stochastic LDSs and LDSs with bounded orbits are addressed. Finally, the problem of deciding whether an energy constraint is satisfied by the weighted orbit, i.e., whether the accumulated weight never drops below a given bound, is analysed.
{"title":"Linear dynamical systems with weight functions","authors":"Rajab Aghamov , Christel Baier , Toghrul Karimov , Joël Ouaknine , Jakob Piribauer","doi":"10.1016/j.nahs.2026.101680","DOIUrl":"10.1016/j.nahs.2026.101680","url":null,"abstract":"<div><div>In discrete-time linear dynamical systems (LDSs), a linear map is repeatedly applied to an initial vector yielding a sequence of vectors called the orbit of the system. A weight function assigning weights to the points in the orbit can be used to model quantitative aspects, such as resource consumption, of a system modelled by an LDS. This paper addresses the problems of how to compute the mean payoff, the total accumulated weight, and the discounted accumulated weight of the orbit under continuous weight functions as well as polynomial weight functions as a special case. Additionally, weight functions that are definable in an o-minimal extension of the theory of the reals with exponentiation, which can be shown to be piecewise continuous, are considered. In particular, good ergodic properties of o-minimal weight functions, instrumental to the computation of the mean payoff, are established. Besides general LDSs, the special cases of stochastic LDSs and LDSs with bounded orbits are addressed. Finally, the problem of deciding whether an energy constraint is satisfied by the weighted orbit, i.e., whether the accumulated weight never drops below a given bound, is analysed.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101680"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077629","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 : 2026-05-01Epub Date: 2025-12-14DOI: 10.1016/j.nahs.2025.101670
Bai Xue
This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability probabilities considered in this paper encompass two aspects: the probability of reaching a set of specified states within a predefined finite time horizon, and the probability of reaching a set of specified states at a particular time instant. The barrier functions presented in this manuscript are developed either by relaxing a parabolic partial differential equation that characterizes the exact reachability probability or by applying the Grönwall’s inequality. In comparison to the prevailing construction method, which relies on Doob’s non-negative supermartingale inequality (or Ville’s inequality), the proposed barrier functions provide stronger alternatives, complement existing methods, or fill gaps.
{"title":"A new framework for bounding reachability probabilities of continuous-time stochastic systems","authors":"Bai Xue","doi":"10.1016/j.nahs.2025.101670","DOIUrl":"10.1016/j.nahs.2025.101670","url":null,"abstract":"<div><div>This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability probabilities considered in this paper encompass two aspects: the probability of reaching a set of specified states within a predefined finite time horizon, and the probability of reaching a set of specified states at a particular time instant. The barrier functions presented in this manuscript are developed either by relaxing a parabolic partial differential equation that characterizes the exact reachability probability or by applying the Grönwall’s inequality. In comparison to the prevailing construction method, which relies on Doob’s non-negative supermartingale inequality (or Ville’s inequality), the proposed barrier functions provide stronger alternatives, complement existing methods, or fill gaps.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101670"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797804","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 : 2026-05-01Epub Date: 2025-12-29DOI: 10.1016/j.nahs.2025.101673
Zhongbin Guo , Qingshuo Song , Guangchen Wang
This paper focuses on a conditional mean-field type game of hybrid switching diffusions systems with delay where both the state dynamics and costs are dependent on the conditional expectations of state given switching process. Firstly, we prove that a nonlinear conditional mean-field anticipated backward stochastic differential equation with regime switching admits a unique solution under mild conditions, which is necessary to guarantee the well-posedness of adjoint equations that arise in the optimality condition for Nash equilibrium point. Then, using established results on conditional mean-field anticipated backward stochastic differential equation, we develop a Pontryagin type maximum principle that provides necessary condition for open-loop Nash equilibrium points. Additionally, we establish two verification theorems under different assumptions, which provide sufficient conditions for Nash equilibrium points. Finally, we present three financial applications. Employing the theoretical results derived, we obtain explicit solutions of all the financial applications and provide some numerical examples with sound economic interpretations for demonstration.
{"title":"A conditional mean-field type stochastic differential game of hybrid switching diffusions systems with delay and its applications","authors":"Zhongbin Guo , Qingshuo Song , Guangchen Wang","doi":"10.1016/j.nahs.2025.101673","DOIUrl":"10.1016/j.nahs.2025.101673","url":null,"abstract":"<div><div>This paper focuses on a conditional mean-field type game of hybrid switching diffusions systems with delay where both the state dynamics and costs are dependent on the conditional expectations of state given switching process. Firstly, we prove that a nonlinear conditional mean-field anticipated backward stochastic differential equation with regime switching admits a unique solution under mild conditions, which is necessary to guarantee the well-posedness of adjoint equations that arise in the optimality condition for Nash equilibrium point. Then, using established results on conditional mean-field anticipated backward stochastic differential equation, we develop a Pontryagin type maximum principle that provides necessary condition for open-loop Nash equilibrium points. Additionally, we establish two verification theorems under different assumptions, which provide sufficient conditions for Nash equilibrium points. Finally, we present three financial applications. Employing the theoretical results derived, we obtain explicit solutions of all the financial applications and provide some numerical examples with sound economic interpretations for demonstration.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101673"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884316","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 : 2026-05-01Epub Date: 2025-12-23DOI: 10.1016/j.nahs.2025.101674
Vassilis Apidopoulos , Cesare Molinari , Juan Peypouquet , Silvia Villa
We introduce and analyze a continuous primal–dual dynamical system in the context of the minimization problem , where and are convex functions and is a linear operator. In this setting, the trajectories of the Arrow–Hurwicz continuous flow may not converge, accumulating at points that are not solutions. Our proposal is inspired by the primal–dual algorithm by Chambolle and Pock (2011), where convergence and splitting on the primal–dual variables are ensured by adequately preconditioning the proximal-point algorithm. We consider a family of preconditioners, which are allowed to depend on time and on the operator , but not on the functions and , and analyze asymptotic properties of the corresponding preconditioned flow. Fast convergence rates for the primal–dual gap and optimality of its (weak) limit points are obtained, in the general case, for asymptotically antisymmetric preconditioners, and, in the case of linearly constrained optimization problems, under milder hypotheses. Numerical examples support our theoretical findings, especially in favor of the antisymmetric preconditioners.
{"title":"Preconditioned primal-dual dynamics in convex optimization: Non-ergodic convergence rates","authors":"Vassilis Apidopoulos , Cesare Molinari , Juan Peypouquet , Silvia Villa","doi":"10.1016/j.nahs.2025.101674","DOIUrl":"10.1016/j.nahs.2025.101674","url":null,"abstract":"<div><div>We introduce and analyze a continuous primal–dual dynamical system in the context of the minimization problem <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>A</mi><mi>x</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>f</mi></math></span> and <span><math><mi>g</mi></math></span> are convex functions and <span><math><mi>A</mi></math></span> is a linear operator. In this setting, the trajectories of the Arrow–Hurwicz continuous flow may not converge, accumulating at points that are not solutions. Our proposal is inspired by the primal–dual algorithm by Chambolle and Pock (2011), where convergence and splitting on the primal–dual variables are ensured by adequately preconditioning the proximal-point algorithm. We consider a family of preconditioners, which are allowed to depend on time and on the operator <span><math><mi>A</mi></math></span>, but not on the functions <span><math><mi>f</mi></math></span> and <span><math><mi>g</mi></math></span>, and analyze asymptotic properties of the corresponding preconditioned flow. Fast convergence rates for the primal–dual gap and optimality of its (weak) limit points are obtained, in the general case, for asymptotically antisymmetric preconditioners, and, in the case of linearly constrained optimization problems, under milder hypotheses. Numerical examples support our theoretical findings, especially in favor of the antisymmetric preconditioners.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101674"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840371","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 : 2026-05-01Epub Date: 2026-01-30DOI: 10.1016/j.nahs.2026.101681
Térence Bayen , Anas Bouali , Loïc Bourdin
In this paper we address the minimum time problem for the double integrator, but here, in contrast with the classical version of this problem, the control is constrained to remain constant as long as the state belongs to a given region of the state space called loss-of-control region. This situation prevents switches from occurring in the loss-of-control region and, therefore, a new analysis has to be performed. For this purpose we prove an appropriate version of the Pontryagin maximum principle in which the necessary conditions comprise two key components. The first is an averaged Hamiltonian gradient condition to determine the optimal constant values of the control in the loss-of-control region. The second is, similarly to hybrid maximum principles found in the literature, that the costate admits discontinuity jumps at the interface between the loss-of-control region and its complement. We then highlight the theoretical use of these necessary conditions by solving analytically the minimum time problem for the double integrator with an illustrative loss-of-control region (precisely, the left vertical half-space). New behaviors are observed such as the lack of dynamic programming principle, of feedback expression and of saturation of the control constraint set. Finally we further illustrate these aspects by solving numerically the same minimum time problem for the double integrator but with two other illustrative loss-of-control regions (first a sloped half-space, then a disk).
{"title":"Minimum time problem for the double integrator with a loss-of-control region","authors":"Térence Bayen , Anas Bouali , Loïc Bourdin","doi":"10.1016/j.nahs.2026.101681","DOIUrl":"10.1016/j.nahs.2026.101681","url":null,"abstract":"<div><div>In this paper we address the minimum time problem for the double integrator, but here, in contrast with the classical version of this problem, the control is constrained to remain constant as long as the state belongs to a given region of the state space called <em>loss-of-control region</em>. This situation prevents switches from occurring in the loss-of-control region and, therefore, a new analysis has to be performed. For this purpose we prove an appropriate version of the Pontryagin maximum principle in which the necessary conditions comprise two key components. The first is an averaged Hamiltonian gradient condition to determine the optimal constant values of the control in the loss-of-control region. The second is, similarly to hybrid maximum principles found in the literature, that the costate admits discontinuity jumps at the interface between the loss-of-control region and its complement. We then highlight the theoretical use of these necessary conditions by solving analytically the minimum time problem for the double integrator with an illustrative loss-of-control region (precisely, the left vertical half-space). New behaviors are observed such as the lack of dynamic programming principle, of feedback expression and of saturation of the control constraint set. Finally we further illustrate these aspects by solving numerically the same minimum time problem for the double integrator but with two other illustrative loss-of-control regions (first a sloped half-space, then a disk).</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101681"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077630","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 : 2026-05-01Epub Date: 2026-01-27DOI: 10.1016/j.nahs.2026.101684
Vladimír Švígler, Jonáš Volek
In this work, we introduce a notion of perfect stationary solutions of reaction–diffusion differential equations on lattices and regular graphs and show its elementary properties. The perfect stationary solutions – a special class of finite-range solutions in which the neighborhood values are determined by the value of the central vertex – generalize periodic stationary solutions. The focus on the solution which attain a finite number of values enables us to reduce the stationary problem from a countable algebraic system of equations to a finite one. However, the possible absence of periodicity in the solutions allows for richer structure of the solutions and their abundance compared to the periodic stationary solutions. We further present results from the theory of perfect colorings in order to prove the existence of the solutions on the square, triangular, and hexagonal grid. As a byproduct, the existence of uncountable number of two-valued stationary solutions on these grids is shown. These two-valued solutions alone can form highly aperiodic and highly irregular patterns. Finally, an application to a bistable reaction–diffusion equation on the square grid is presented.
{"title":"Perfect stationary solutions of reaction–diffusion equations on lattices and regular graphs","authors":"Vladimír Švígler, Jonáš Volek","doi":"10.1016/j.nahs.2026.101684","DOIUrl":"10.1016/j.nahs.2026.101684","url":null,"abstract":"<div><div>In this work, we introduce a notion of perfect stationary solutions of reaction–diffusion differential equations on lattices and regular graphs and show its elementary properties. The perfect stationary solutions – a special class of finite-range solutions in which the neighborhood values are determined by the value of the central vertex – generalize periodic stationary solutions. The focus on the solution which attain a finite number of values enables us to reduce the stationary problem from a countable algebraic system of equations to a finite one. However, the possible absence of periodicity in the solutions allows for richer structure of the solutions and their abundance compared to the periodic stationary solutions. We further present results from the theory of perfect colorings in order to prove the existence of the solutions on the square, triangular, and hexagonal grid. As a byproduct, the existence of uncountable number of two-valued stationary solutions on these grids is shown. These two-valued solutions alone can form highly aperiodic and highly irregular patterns. Finally, an application to a bistable reaction–diffusion equation on the square grid is presented.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101684"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077705","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 : 2026-05-01Epub Date: 2026-01-27DOI: 10.1016/j.nahs.2026.101683
Mircea Şuşcă , Vlad Mihaly , Zsófia Lendek , Irinel-Constantin Morărescu , Petru Dobra
We consider the classical emulation paradigm in which a controller is already designed for a linear time-invariant plant. Motivated by implementation constraints in real applications, we analyze the effects of ubiquitous low-cost quantizers on the closed-loop dynamics. Consequently, we address the robust control problem of an uncertain discrete-time linear process using a regulator affected by the effects of uniform quantization performed by the input–output converters and arithmetical unit. In this setup with fixed hardware resolutions, the regulator’s state-space realization is balanced to minimize the process’ state quantization error while simultaneously maintaining its desired transient response. To characterize the quantization error, we provide an ultimate bound for its worst-case scenario using the input-to-state stability framework. The minimization is performed using off-the-shelf tools, with a characterization of the resulting problem. Finally, a comparative numeric case study showing the tightness of the computed bound is discussed.
{"title":"Controller redesign to minimize uniform quantization errors in uncertain linear systems with fixed hardware constraints","authors":"Mircea Şuşcă , Vlad Mihaly , Zsófia Lendek , Irinel-Constantin Morărescu , Petru Dobra","doi":"10.1016/j.nahs.2026.101683","DOIUrl":"10.1016/j.nahs.2026.101683","url":null,"abstract":"<div><div>We consider the classical emulation paradigm in which a controller is already designed for a linear time-invariant plant. Motivated by implementation constraints in real applications, we analyze the effects of ubiquitous low-cost quantizers on the closed-loop dynamics. Consequently, we address the robust control problem of an uncertain discrete-time linear process using a regulator affected by the effects of uniform quantization performed by the input–output converters and arithmetical unit. In this setup with fixed hardware resolutions, the regulator’s state-space realization is balanced to minimize the process’ state quantization error while simultaneously maintaining its desired transient response. To characterize the quantization error, we provide an ultimate bound for its worst-case scenario using the input-to-state stability framework. The minimization is performed using off-the-shelf tools, with a characterization of the resulting problem. Finally, a comparative numeric case study showing the tightness of the computed bound is discussed.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101683"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077628","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 : 2026-05-01Epub Date: 2025-12-08DOI: 10.1016/j.nahs.2025.101672
Aya Younes, Félix Miranda-Villatoro, Bernard Brogliato
This article is largely concerned with the trajectory tracking control of frictional oscillators, which are nonsmooth nonlinear dynamical systems. The trajectory tracking problem, which is studied under a passivity-based controller addresses three main cases: the nominal case with known friction coefficient, uncertain friction coefficient, and when the Coulomb friction model is enhanced by including Stribeck effects. Monotonicity (or hypomonotonicity) of the friction model is crucial for the stability analysis of the tracking error. It can be relaxed to hypomonotonicity to handle Stribeck model. The framework of linear complementarity systems is used for the analysis. The case of a two-mass system is tackled as an extension of the standard one-mass oscillator. Theoretical results are supported by numerical simulations.
{"title":"Passivity-based trajectory tracking control in frictional oscillators with set-valued friction","authors":"Aya Younes, Félix Miranda-Villatoro, Bernard Brogliato","doi":"10.1016/j.nahs.2025.101672","DOIUrl":"10.1016/j.nahs.2025.101672","url":null,"abstract":"<div><div>This article is largely concerned with the trajectory tracking control of frictional oscillators, which are nonsmooth nonlinear dynamical systems. The trajectory tracking problem, which is studied under a passivity-based controller addresses three main cases: the nominal case with known friction coefficient, uncertain friction coefficient, and when the Coulomb friction model is enhanced by including Stribeck effects. Monotonicity (or hypomonotonicity) of the friction model is crucial for the stability analysis of the tracking error. It can be relaxed to hypomonotonicity to handle Stribeck model. The framework of linear complementarity systems is used for the analysis. The case of a two-mass system is tackled as an extension of the standard one-mass oscillator. Theoretical results are supported by numerical simulations.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101672"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749774","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 : 2026-05-01Epub Date: 2025-12-07DOI: 10.1016/j.nahs.2025.101671
Wenjie Cao , Fuke Wu
This paper focuses on the averaging principle for a class of singularly perturbed stochastic systems, in which the slow process is a diffusion process, and fast process is a purely jumping process in an infinitely countable state space and its transition probability depends on the slow component. By using the solution of the Poisson equation as a corrector and the martingale method, the diffusion approximation of this singularly perturbed stochastic system is established.
{"title":"Weak convergence and diffusion approximation of singularly perturbed stochastic differential equation with state-dependent switching","authors":"Wenjie Cao , Fuke Wu","doi":"10.1016/j.nahs.2025.101671","DOIUrl":"10.1016/j.nahs.2025.101671","url":null,"abstract":"<div><div>This paper focuses on the averaging principle for a class of singularly perturbed stochastic systems, in which the slow process is a diffusion process, and fast process is a purely jumping process in an infinitely countable state space and its transition probability depends on the slow component. By using the solution of the Poisson equation as a corrector and the martingale method, the diffusion approximation of this singularly perturbed stochastic system is established.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"60 ","pages":"Article 101671"},"PeriodicalIF":3.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749775","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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