Open AccessRobust finite‐time H ∞ control for uncertain discrete‐time singular systems with Markovian jumps
Author(s) -
Zhang Yingqi,
Shi Peng,
Nguang Sing Kiong,
Song Yongduan
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2013.1013
Subject(s) - mathematics , discrete time and continuous time , singular solution , control theory (sociology) , bounded function , markov process , stability (learning theory) , mathematical analysis , control (management) , computer science , statistics , artificial intelligence , machine learning
This study is concerned with the finite‐time H ∞ control problem for uncertain discrete‐time Markovian jump singular systems with time‐varying norm‐bounded disturbance. Firstly, the concepts of singular finite‐time stability, singular finite‐time boundedness and singular H ∞ finite‐time stabilisation are given. Then, sufficient conditions of singular finite‐time boundedness and singular H ∞ finite‐time stability are derived for the class of discrete‐time Markovian jump singular systems. The main contribution of the study is to propose a numerical efficient and reliable controller design process for state feedback finite‐time H ∞ control of discrete‐time Markovian jump singular systems. By applying the descriptor system technique presented by Fridman and Shaked, sufficient criteria are presented for the solvability of the problems, which can be reduced to feasibility problems in terms of linear matrix inequalities. Finally, numerical examples are included to illustrate the validity of the presented results.