Robust finite-time H ∞ control for uncertain discrete-time singular systems with Markovian jumps

Yingqi Zhang; Peng Shi; Sing Kiong Nguang; Yongduan Song

Robust finite-time H _∞ control for uncertain discrete-time singular systems with Markovian jumps

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Author(s): Yingqi Zhang ¹ ; Peng Shi ^{2, 3} ; Sing Kiong Nguang ⁴ ; Yongduan Song ⁵
- Affiliations: 1: College of Science, Henan University of Technology, Zhengzhou 450001, People's Republic of China;
  2: School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005, Australia;
  3: College of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia;
  4: Department of Electrical and Computer Engineering, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand;
  5: School of Automation, Chongqing University, Chongqing 400044, People's Republic of China
Source: Volume 8, Issue 12, 14 August 2014, p. 1105 – 1111
DOI: 10.1049/iet-cta.2013.1013 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 01/08/2013, Accepted 13/01/2014, Published 09/06/2014

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.

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Robust finite-time H _∞ control for uncertain discrete-time singular systems with Markovian jumps

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