Stability analysis and stabilization of semi-Markov jump linear systems with unavailable sojourn-time information  

作　　者：Xiaotai WU Yang TANG Shuai MAO Ying ZHAO 

机构地区：[1]School of Mathematics and Physics,Anhui Polytechnic University,Wuhu 241000,China [2]Key Laboratory of Advanced Control and Optimization for Chemical Processes,Ministry of Education,East China University of Science and Technology,Shanghai 200237,China

出　　处：《Science China(Information Sciences)》2024年第7期207-219,共13页中国科学（信息科学）（英文版）

基　　金：supported in part by National Natural Science Foundation of China (Grant Nos. 61751305, 61873294);Talent Programme of Anhui province;Programme of Shanghai Academic Research Leader (Grant No. 20XD1401300)

摘　　要：This study addresses the stability and stabilization problems of discrete-time semi-Markov jump linear systems(S-MJLSs)with unavailable sojourn-time information.The sojourn-time probability mass functions(S-TPMFs)of discrete-time semi-Markov chains are no longer confined to the geometric distribution,and it is difficult to obtain accurate and comprehensive information for S-TPMFs in practice.This is because S-TPMFs are usually deduced from the statistical characteristics according to the sampled-data,while adequate samples are often costly and time consuming.In this study,when the S-TPMFs for semi-Markov chains are assumed to be unavailable,theσ-error mean square stability is investigated for discrete-time SMJLSs with some widely used assumptions;for semi-Markov chains,only the transition probability matrix of the embedded chain is used.In addition,the existence conditions of the effective controller are provided for closed-loop systems without using the information of S-TPMFs.Numerical examples are presented to illustrate the validity of the obtained theoretical results.

关 键 词：semi-Markov chain semi-Markov jump linear systems σ-error mean square stability unavailable sojourn-time information 

分 类 号：O211.62[理学—概率论与数理统计] O231[理学—数学]