Modeling And Stability Analysis Of Stochastic Hybrid Systems

With the development of intelligent system and digital information,the control system gets more and more complex,including not only continuous and determined dynamic process,but also a large number of discrete variables and random element.In that way,the study of stochastic hybrid systems has gradually been in a hot research because of its great practical value.This paper studies the semi-Markov impulsive jump system,one of the most practical and extensively researched subsystem in stochastic hybrid system,mainly including:Firstly,the stochastic stability of semi-Markov impulsive jump system has been studied,and multiple Lyapunov function approach is used to propose less conservative sufficient conditions for stability.Futher for semi-Markov impulsive jump system with Weibull distribution of the sojourn-time,the numerically testable sufficient conditions are given via partitioning the upper and lower bounds of the time-varying transition rate,and an optimized partitioning method is derived.Based on the above theories,the state feedback controller is designed to stabilize unstable systems.Secondly,the foregoing theories are extended to the uncertain semi-Markov impulsive jump system with both uncertain system structure and uncertainty in the transition rate.The stochastic stability of it is discussed by constructing a suitable Lyapunov function and LMI tools,and a robust controller with dynamical compensation affect is designed.At last,the sufficient conditions for finite time stability of uncertain system are also studied.Finally,the results above mentioned are applied to a rotary inverted pendulum control system.Based on the mathematical model of generalized object including a DC motor,the stochastic stability problems of active fault tolerant system with the actuator failures,are discussed.Furthermore,to deal with the transport delay and packet loss of its control network,a unified iterative model is established and designed a impulsive controller to achieve a stochastic stabilization and finite time stabilization.