New Approach to Feedback Stabilization of Linear Discrete Time-Varying Stochastic Systems

• 成果类型: Article
• 署名作者: Zhang, Tianliang; Xu, Shengyuan; Zhang, Weihai
• 署名单位: Qingdao University of Technology; Nanjing University of Science & Technology; Nanjing University of Science & Technology; Shandong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3482119
• 发表日期: 2025
• 页码: 2004-2011
• 关键词: Stability criteria; Stochastic systems; asymptotic stability; Time-varying systems; vectors; Closed loop systems; Symmetric matrices; Linear matrix inequalities; Indium tin oxide; automation; Linear discrete time-varying stochastic systems; mean square uniform asymptotic/exponential stabilization (MSUAS/MSUES); mean square uniform stabilization (MSUS); state transition matrix (STM); uniform finite-time stabilization (UFTS)

摘要

This article investigates uniform finite-time stabilization, mean square uniform stabilization, and mean square uniform asymptotic/exponential stabilization of linear discrete time-varying stochastic (LDTVS) systems. A new state transition matrix (STM) method is first used to study the feedback stabilization problem of LDTVS systems. Based on the STM method, necessary and sufficient conditions for the above concerned feedback stabilization issues are, respectively, presented in terms of STMs and generalized constrained Lyapunov equations/inequalities. More importantly, linear matrix inequality-based necessary and sufficient conditions are provided for uniform finite-time stabilization and mean square uniform stabilization, which are very convenient in the controller design. A practical example is proposed to show the effectiveness of our main results.