Stability analysis of semi-Markov switching stochastic mode-dependent delay systems with unstable subsystems?

This paper is dedicated to studying the stability of semi-Markov switching stochastic delay systems with unstable subsystems, where delay depends on another semi-Markovian process and transition rates are uncertain. Based on the stochastic analysis theory and the mode-dependent multi-Lyapunov function method, relevant sufficient conditions are established to ensure the asymptotic stability in mean square of the system. In addition, contrary to the existing works, the system under consider is more general and our works are not only applicable to the system with partial unstable subsystems, but also applicable to the system with all unstable subsystems. Finally, one numerical example is provided to illustrate the correctness of the method described in the paper.