Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay

The stochastic stability and stabilisation problems of a Markov jump system (MJS) with time-delay under a dynamical output feedback control law is considered. LMI-based sufficient conditions are established for the system to be stochastic stable and exponentially stable. A sufficient and necessary condition for the MJS to be stabilisable in the mean square quadratic stable sense, which implies stochastic stability of the system, is established. An LMI-based control design method is proposed and a numerical example is included to show the usefulness of the theoretical results.