Stochastic finite-time stabilization of discrete-time positive Markov jump linear systems with time-delay

This paper deals with stochastic finite-time stabilization of a discrete-time positive Markov jump linear system with time-delay. Firstly, the stochastic finite-time stability of the positive Markov jump linear system with time-delay is proved to be equivalent to the finite-time stability of a deterministic positive linear system with time-delay, as well as the finite-time stability of a deterministic positive linear system without time-delay. Secondly, a new sufficient condition for the stochastic finite-time stability of the discrete-time positive Markov jump linear system with time-delay is obtained resorting to the finite-time stability condition of the deterministic positive linear system. Thirdly, the stochastic finite-time state feedback stabilization condition is proposed by solving a linear programming problem. Lastly, a numerical example is given to validate the design method.