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Zbl 1093.93026
Xiong, Junlin; Lam, James; Gao, Huijun; Ho, Daniel W.C.
On robust stabilization of Markovian jump systems with uncertain switching probabilities. (English)
[J] Automatica 41, No. 5, 897-903 (2005). ISSN 0005-1098

Summary: This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.

MSC 2000:: *93D21 Adaptive and robust stabilization
93E15 Stochastic stability

Keywords: Linear matrix inequalities; Markovian parameters; Robust stability; Uncertain systems

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