Stability analysis and controller synthesis of continuous-time nonhomogeneous Markovian jump systems with state and input delays

Abstract

This paper focuses on the problems of stability analysis and controller synthesis for a class of nonhomogeneous Markovian jump systems with both state and input delays. The time-varying transition rate matrix is described as a polytope set. By constructing a Lyapnouv–Krasovskii functional and introducing some appropriately slack matrices, a stochastic stability condition is proposed in term of infinite matrix inequalities. Based on this, a new stochastic stability condition is further derived in form of a finite set of LMIs. Then, in terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of state-feedback controller is presented and proved. Finally, three numerical examples are provided to illustrate the effectiveness and usefulness of the obtained results.