Stability and stabilisation of Markovian jump systems under fast switching: an averaging approach  

作　　者：Guoliang Wang Yande Zhang Yunshuai Ren 

机构地区：[1]School of Information and Control Engineering,Liaoning Petrochemical University,Fushun,Liaoning,People’s Republic of China

出　　处：《Journal of Control and Decision》2023年第4期572-583,共12页控制与决策学报（英文）

基　　金：supported by the Open Project of Key Field Alliance of Liaoning Province[grant number 2022-KF-11-03].

摘　　要：ABSTRACTThis paper addresses the problems of stability and stabilisation of Markovian jump systems(MJSs) with fast switching. First, a novel model by applying an averaging approach to the fastswitching is proposed. Then, a new method for constructing an auxiliary system is given to makethe stability analysis. It is proved that the stability of the originally fast switching MJS couldbe guaranteed by an MJS with an average switching, if the fast switching achieves its averageapproximation sufficiently fast. Based on the proposed results, some extensions about generally stabilising controllers are considered, where the fault-tolerant situation is involved too.All the conditions are presented in terms of LMIs. Finally, two numerical examples are used todemonstrate the effectiveness and superiority of the method.

关 键 词：Markovian jump systems fast switching averaging approach STABILITY stabilisation linear matrix inequalities(LMIs) 

分 类 号：O211.62[理学—概率论与数理统计] TP3[理学—数学]