Analysis of stability and robust stability for stochastic hybrid systems with impulsive effects

Abstract

In this article, the problems of stability and robust stability analysis are investigated for a class of Markovian switching stochastic systems, which has impulses at switching instants. The switching parameters considered form a continuous-time discrete-state homogeneous Markov process. Multiple Lyapunov techniques are used to derive sufficient conditions for stability in probability of the overall system. The conditions are in linear matrix inequalities form, and can be used to solve stabilization synthesis problems. The results are extended to the design of a robust-stabilized state-feedback controller as well. A numerical example shows the effectiveness of the proposed approach.

Keywords

impulsive system / Markovian switching / stable in probability / linear matrix inequality (LMI) / robust stability

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Higher Education Press and Springer-Verlag Berlin Heidelberg