A LYAPUNOV-METZLER CONDITION FOR ALMOST SURE STABILITY OF MARKOV JUMP LINEAR SYSTEMS

In this paper we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A new sufficient condition is derived based on an extended Lyapunov-Metzler inequality. This condition is proven to be less conservative with respect to the existing sufficient conditions. The inequalities generalize those associated with mean square stability and establish a clear link between the two notions. The problem of almost sure stabilizability and detectability is finally discussed.