具有饱和输入的半马尔可夫线性系统的几乎必然指数稳定性分析
Analysis of Almost Sure Exponential Stability for Semi-Markovian Linear Systems with Saturated Inputs
摘要: 随机切换系统作为模拟受随机结构变化影响的动态过程的特殊混合系统，在众多领域具有广泛应用。马尔可夫线性系统(MLSs)作为重要模型备受关注，然而其逗留时间服从指数分布且转换速率恒定，限制了其应用范围。为克服这些限制，引入了半马尔可夫线性系统(S-MLSs)，其适用性更为广泛，允许子系统的逗留时间和转换速率是时变的。本文针对S-MLSs的几乎必然指数稳定性问题展开探讨，采用了线性矩阵不等式(LMIs)技术解决控制问题。我们提出了新的稳定性充分条件，改进了现有研究并减少了保守性。然而，目前的研究忽视了执行器饱和问题，这在实践中不可避免且严重影响闭环系统的性能。因此，本文旨在解决受随机扰动和执行器饱和影响的S-MLSs的几乎必然指数稳定问题，填补了该领域的研究空白。
Abstract: Random switching systems, as special hybrid systems simulating dynamic processes affected by stochastic structural changes, have wide applications in numerous fields. While Markovian Linear Systems (MLSs) have garnered significant attention as important models, their applicability is constrained by the assumption that dwell times follow an exponential distribution and transition rates remain constant. To overcome these limitations, Semi-Markovian Linear Systems (S-MLSs) have been introduced, offering broader applicability by allowing the dwell times and transition rates of subsystems to be time-varying. This paper addresses the almost sure exponential stability problem of S-MLSs, employing Linear Matrix Inequality (LMI) techniques to tackle the control problem. We propose novel stability sufficient conditions, improving upon existing research and reducing conservatism. However, current studies overlook the issue of actuator saturation, which is inevitable in practice and significantly impacts the performance of closed-loop systems. Therefore, this paper aims to address the almost sure exponential stability problem of S-MLSs subject to both stochastic perturbations and actuator saturation effects, filling a research gap in this field.
文章引用：闫咏春. 具有饱和输入的半马尔可夫线性系统的几乎必然指数稳定性分析[J]. 理论数学, 2024, 14(4): 332-341. https://doi.org/10.12677/pm.2024.144141

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