Stochastic finite-time L1-gain control for positive Markov jump linear systems with interval time-varying delay

This paper is concerned with the stochastic finite-time L1-gain control problem for positive Markov jump linear systems with interval time-varying delay and partly known transition rates. By constructing an appropriate linear co-positive stochastic Lyapunov functional, some delay-dependent sufficient conditions of the stochastic finite-time boundedness and finite-time L1-gain performance are developed, respectively. Then a stochastic finite-time state feedback L1-gain controller is designed by means of linear programming such that the closed-loop system is positive and stochastically finite-time bounded with finite-time L1-gain performance. The effectiveness of the method is verified by an example.