Robust Stochastic Stabilization for Positive Markov Jump Systems with Actuator Saturation

This paper is concerned with robust stochastic stabilization for positive Markov jump systems with actuator saturation. The considered systems contain interval and polytopic uncertainties, respectively. First, a stochastic co-positive Lyapunov functional is constructed for the systems. By virtue of the presented Lyapunov functional, a new controller design approach is addressed using matrix decomposition technique. Under the designed controller, robust stochastic stabilization of the systems with interval and polytopic uncertainties is achieved, respectively. Furthermore, an effective method for estimating the attraction domain is established by solving an optimization problem. An implemental algorithm is provided based on linear programming to solve the corresponding conditions. Finally, two numerical examples are provided to illustrate the reduced conservatism and effectiveness of the proposed design.