Stability Analysis And H_? Control For Nonlinear Continuous Time Singular Markov Jump System Subject To Actuator Saturation

Markov jump systems(MJSs)can model stochastic systems with abrubt structural variation resulting from the occurrence of some inner discrete events in the systems such as manufacturing systems,networked control systems.Its dynamics are driven by not only time but also discrete events which are regard as system modes in MJSs and stochastic jump among the systems modes is described by a Markov process.It has strong paractical background,has been widely favored by the majority of scholars.In recent years,many problems about the systems have been solved.Therefore,the research of MJSs not only has theoretical significance,but also has practical engineering value.In this paper,stability and H_? control for continuous time Markov jump systems subject to actutor saturation are considered.The main contributions of this dissertation are as follows:(1)The stability for continuous time singular MJSs subject to actuator saturation is discussed.Based on the implicit function theorem,linear matrix inequalities suffcient conditions are developed which guarantee that the sys-tems are regular,impulse-free,have unique solution in a neighborhood of the origin,and with the infinitesimal generator for stochastic Lyapunov function of the MJSs,and transition probability,conditions are obtained to guarantee this kind of systems are stochastically admissible.With the conditions,LMI optimization problem is obtained,and the state feedback controller can be reached by solving the LMI optimization problem.And a numerical example illustrates the effectiveness.(2)The H_? performance for continuous time singular MJSs subject to actuator saturation is discussed.The design of H_? state feedback controller of closed systems is developed based on LMI technique.The sufficient conditions for the performance of the closed-loop system with saturation control and H_? state feedback controller are given.A strict linear matrix inequalities optimization problem is developed to solve the H_? control problemand design the H_? state feedback controller.And a numerical example illustrates the effectiveness.