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Stability analysis of switched stochastic systems. (English) Zbl 1209.93157
Summary: For a class of Switched Stochastic (SS) systems, the Moment Stability (M-S) and Sample Path Stability (SP-S) are investigated, respectively, and there are two main contributions. First, based on accurate estimations for the powers of solution of a special nonswitched stochastic system, by employing the concepts of a Lyapunov function and describing the switching laws with the average dwell-time and the subsystems, three sufficiency theorems of $p$-th M-S are given for the SS systems. Then, for the SP-S of such systems, based on the results of $p$-th M-S, two sufficiency theorems are obtained for $p>2$ and $p=2$, respectively.
##### MSC:
 93E15 Stochastic stability 93D30 Scalar and vector Lyapunov functions 93E03 General theory of stochastic systems