Exponential stability analysis of discrete-time almost periodic piecewise nonlinear systems

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems Pub Date : 2025-09-18 DOI:10.1016/j.nahs.2025.101642

Xiaoyun Wei , Xingwen Liu , Jun Yang , Tingjin Liu

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引用次数: 0

Abstract

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.

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离散时间概周期分段非线性系统的指数稳定性分析

研究了具有不确定停留时间的离散几乎周期分段非线性系统的指数稳定性分析。离散时间APPNS有一个基本周期，在此期间，构成系统的有限数量的子系统被循环激活。这样的系统可以被建模为具有循环开关信号的开关系统。在假定离散时间APPNSs各子系统的向量场连续可微的前提下，首先利用Lyapunov定理验证了离散时间APPNSs的指数稳定性。然后，采用线性化方法，构造混合模时变齐次Lyapunov函数，导出用线性矩阵不等式（lmi）表示的特定稳定性条件。注意，这个条件可以验证所考虑的非线性系统的指数稳定性，以及相应的线性化系统的指数稳定性。此外，本文所采用的线性化方法也适用于一般的开关系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Hybrid Systems AUTOMATION & CONTROL SYSTEMS-MATHEMATICS, APPLIED

CiteScore

8.30

自引率

9.50%

发文量

审稿时长

>12 weeks

期刊介绍： Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.