Stability analysis of switched Markov jump linear systems with hybrid switchings

This paper investigates the exponentially almost sure (EAS) stability of switched Markov jump linear systems (SMJLSs), which is subjected to deterministic switching and stochastic Markov jump switching. Using the ergodic law of large numbers, stability criteria for the SMJLS with all EAS stable or partially unstable sub-Markov jump linear systems are established, where the deterministic switching is governed by a Phi-dependent average dwell time approach. Some stability conditions under the average dwell time and mode-dependent average dwell time (MDADT) deterministic switching are established as corollaries. Especially, the results of MDADT for SMJLS are given for the first time. Finally, three numerical examples are provided to illustrate the efficiency of the proposed results.