State feedback stabilization for linear systems with time-varying delays and input saturation: A Markov jump model approach

This paper is concerned with the state feedback stabilization problem for delayed systems with input saturation. Based on the stochastic property of time-varying delays, the considered system can be transformed into a continuous Markov jump system with stochastic delays, where the growth trend and the maximum value of the time-varying delays are limited. The aim is to design a state feedback controller which can switch with time-varying delay in terms of Markov process, such that the system is exponentially mean-square stable. Conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities(LMIs). When these LMIs are feasible, the desired robust controller is given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.