No abstract

Abstract-The robust stabilization problem is investigated for a class of delta operator formulated Markovian jump systems with time-varying delays. The aim is to design a state feedback controller which can make the closed-loop system stochastic asymptotically stable in delta domain. A sufficient condition of the existence of such controllers is obtained by the linear matrix inequality approach and a design procedure of such controllers is presented. Furthermore, the proposed method can unify some previous related continuous and discrete systems into the framework on operator systems. A numerical example is provided to demonstrate availability and efficiency of the design method.Keywords-robust stochastic stabilization, Markovian jump system, delta operator system, time-varying delays I. INTRODUCTION Goodwin constructed delta operator instead of traditional shift operator for sampling continuous systems in [1]. The proposed method can unify some previous related results of the continuous and discrete systems into the frame-work of the delta operator systems framework. A class of system in delta domain has been investigated in [2][3][4]. The problem of system instability when the sampling time is fast can be solved by using delta operator model [5]. It also has been shown better numerical properties by using delta operator than using shift operator at high sampling rate [6].