Equivalence between Mean square, Stochastic and Exponential stability for Singular jump linear systems

This paper studies Mean square stability, Stochastic stability and Exponential stability for discrete-time singular linear systems whose parameters are driven by a finite state Markov chain. It is shown the equivalence of these notions under certain conditions. New necessary conditions for mean square stability in terms of generalized Lyapunov equations for homogeneous and non-homogeneous of this class of systems are also given.