Robust Stability Analysis of Linear Parameter-Varying Systems With Markov Jumps

• 成果类型: Article
• 署名作者: Vargas, Alessandro N.; Agulhari, Cristiano M.; Oliveira, Ricardo C. L. F.; Preciado, Victor M.
• 署名单位: Universidade Tecnologica Federal do Parana; Universidade Estadual de Campinas; University of Pennsylvania
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3132231
• 发表日期: 2022
• 页码: 6234-6239
• 关键词: Markov processes; Stability criteria; robust stability; Linear matrix inequalities; Linear systems; Symmetric matrices; Stochastic systems; Linear matrix inequalities (LMIs); linear parameter-varying systems; Markov jump linear systems (MJLSs); polytopic uncertainty; stochastic stability

摘要

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article's contribution.