Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

Abstract

This paper investigated the almost surely exponential stability (ES a.s.) for semi‐Markovian switched singular stochastic systems (SSSSs) with mode‐dependent ranks, in which the derivative matrices Ei have different ranks. Due to the constraint of consistent initial conditions, state jumps may occur at switching instants in switched singular systems. Some more general conditions for the existence and uniqueness of the solution of semi‐Markovian SSSSs with mode‐dependent ranks are given together with a detailed analysis of state jumps. Based on the equivalent systems transformation and multiple Lyapunov functions method, novel conditions of ES a.s. are presented for addressed systems. An example is given to explain the effectiveness of developed results.