Robust control of time-delayed stochastic switched systems with dwell

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2024-10-14 DOI:10.1016/j.sysconle.2024.105934

E. Gershon , L.I. Allerhand , U. Shaked

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引用次数: 0

Abstract

Linear, state-delayed, discrete-time, stochastic, switched systems are considered, where the problems of stochastic

l_{2}

-gain and state-feedback control designs are treated and solved. We first develop a special version of a bounded real lemma for the said systems for the nominal case.

Based on the this lemma we derive state-feedback gains for nominal systems where in our solution method, to each subsystem of the switched system, a Lyapunov function is assigned that is non-increasing at the switching instants and where a dwell time constrain is imposed on the system. The assigned Lyapunov function is allowed to vary piecewise linearly in time, starting at the end of the previous switch instant, and it becomes time-invariant after the dwell. Based on the solution of the state-feedback control for nominal systems and exploiting the fact that this solution is affine in the system matrices, a state-feedback control is derived for the polytopic case. We bring a numerical example that demonstrates the solvability and tractability of our solution method.

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带停留的时延随机切换系统的鲁棒控制

我们考虑了线性、状态延迟、离散时间、随机、开关系统，处理并解决了随机 l2 增益和状态反馈控制设计问题。我们首先为上述名义系统开发了一个特殊版本的有界实数定理。基于该定理，我们推导出了名义系统的状态反馈增益，在我们的求解方法中，为开关系统的每个子系统分配了一个在开关时刻非递增的 Lyapunov 函数，并对系统施加了停留时间限制。分配的 Lyapunov 函数从上一个切换瞬间结束时开始，允许在时间上片断线性变化，停留时间结束后，Lyapunov 函数变得与时间无关。根据标称系统的状态反馈控制解法，并利用该解法在系统矩阵中的仿射关系，我们得出了多拓扑情况下的状态反馈控制。我们通过一个数值示例证明了我们的求解方法的可解性和可操作性。

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

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.