Robust finite-time H ∞ control for uncertain singular stochastic Markovian jump systems via proportional differential control law

Li Li; Qingling Zhang; Jian Li; Guoliang Wang

Robust finite-time H _∞ control for uncertain singular stochastic Markovian jump systems via proportional differential control law

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Author(s): Li Li ^{1, 2} ; Qingling Zhang ^{1, 3} ; Jian Li ¹ ; Guoliang Wang ⁴
- Affiliations: 1: Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110819, People's Republic of China;
  2: College of Mathematics, Physics, Bohai University, Jinzhou, Liaoning 121013, People's Republic of China;
  3: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning 110819, People's Republic of China;
  4: School of Information and Control Engineering, Liaoning Shihua University, Fushun, Liaoning 113001, People's Republic of China
Source: Volume 8, Issue 16, 06 November 2014, p. 1625 – 1638
DOI: 10.1049/iet-cta.2014.0194 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 18/09/2013, Accepted 22/05/2014, Revised 14/05/2014, Published 06/08/2014

This study focuses on the problem of robust finite-time H _∞ control for a class of uncertain singular stochastic Markovian jump systems with partially unknown transition rates via proportional differential control law (PDLC). The uncertainties are not only in state matrices and input matrices but also in differential matrices. New sufficient conditions for the existence of mode-dependent PDLC are derived in the form of strict linear matrix inequalities, such that the closed-loop system of the singular stochastic Markovian jump system is not only stochastic finite-time stable but also satisfies a prescribed performance. Numerical examples are used to show the effectiveness of the proposed methods.

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Robust finite-time H _∞ control for uncertain singular stochastic Markovian jump systems via proportional differential control law

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