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Robust Stochastic Stability and H ∞ Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise
Author(s) -
Zhao Yong,
Zhang Weihai,
Xia Jianwei,
Zhang Tianliang
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1543
Subject(s) - control theory (sociology) , mathematics , robust control , multiplicative noise , quadratic equation , stability (learning theory) , multiplicative function , controller (irrigation) , stability theory , control system , computer science , control (management) , engineering , mathematical analysis , nonlinear system , signal transfer function , artificial intelligence , analog signal , biology , geometry , agronomy , physics , digital signal processing , computer hardware , electrical engineering , quantum mechanics , machine learning
This paper focuses on the problems of robust stability and stabilization and robustH ∞control for uncertain singular Markovian jump systems with ( x , v )‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robustH ∞control problem are derived. The desired state feedbackH ∞controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribedH ∞performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.