New results for the stability analysis of two-layer stochastic switched systems

This paper gives a new perspective for the stability analysis of a class of two-layer stochastic switched systems (TLSSSs). In the considered TLSSS, the upper layer system can be regarded as a semi-Markov jump system, in which the arbitrary switching is embedded in the corresponding latent subsystems. A new stability analysis method based on the switched transfer function matrix and ergodic property of the semi-Markov process is proposed to tackle difficulties caused by the complex nature of TLSSSs. Under such a framework, auxiliary systems are constructed for upper layer systems through the corresponding eigenvalues, and the latent subsystems of each auxiliary system are associated with the switched transfer function matrix. Then, the relations between the Lyapunov functions and prescribed system parameters are constructed to deal with the instability caused by the mode jumping. By comprehensively utilizing the property of the semi-Markov process and the above-mentioned methods, sufficient conditions are further presented to ensure the exponential mean-square (EMS) stability and exponential almost sure (EAS) stability, respectively. A numerical example is given to illustrate the effectiveness of the proposed methods.