Robust Finite-time Control For Descriptor Time-Varying Markov Jump Systems

Descriptor time-varying Markov jump system is a kind of system which can effectively describe the parameter mutation.There is no specific rule to follow in the process of its state jumping from one mode to another.The transformation between modes is random,but it obeys Markov jump process.Markov system model can describe many practical systems,such as network system,robot operating system,aerospace system and so on.In this paper,sufficient conditions are obtained to ensure stability of the robust finite-time for descriptor Markovian jump systems with impulsive effects and time-varying norm-bounded disturbance,especially,when the system is in actuator saturation.Using the theory of Lyapunov function and the concept of convex hull based representation of saturation function.The state feedback controller is designed and estimation of domain of attraction is obtained,the results of are extended to convex optimization problems,the solvability condition of the above controller can be equivalent to a feasibility problem of coupled linear matrix inequalities(LMIs).For a Descriptor time-varying nonlinear Markov jump system with actuator saturation,the problem of robust finite-time control is studied when impulse effects and time-domain norm bounded disturbances exist in the system.By introducing the discontinuous time-varying Lyapunov-Krasovkii function associated with impulsive time series and using linear matrix inequality(LMI)technique,sufficient conditions are obtained to ensure robust time-domain stability and H_?boundedness of the system.Then,through the non-fragile H_?control technology,the analysis and design of the non-fragile robust H_?finite-time state feedback controller are given to realize the time-domain H_?control of the system.