Premium
Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information
Author(s) -
Li Zhicheng,
Xu Yinliang,
Fei Zhongyang,
Huang Hong,
Misra Satyajayant
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3854
Subject(s) - control theory (sociology) , stability (learning theory) , mathematics , controller (irrigation) , stability criterion , linear matrix inequality , circle criterion , mathematical optimization , exponential stability , control (management) , computer science , nonlinear system , statistics , physics , discrete time and continuous time , quantum mechanics , machine learning , artificial intelligence , agronomy , biology
Summary The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.