Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

• 成果类型: Article
• 署名作者: Wang, Bao; Zhu, Quanxin; Li, Subei
• 署名单位: Xuzhou University of Technology; Hunan Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3272190
• 发表日期: 2024
• 页码: 1952-1959
• 关键词: sigma-error mean square stability; Emission probability; hidden semi-Markov chain (SMC); observed mode-dependent controller; semi-Markov kernel (SMK)

摘要

This article studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the abovementioned conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode-dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.