Stability And Control Of Impulsive Stochastic Systems And Impulsive Switched Systems

The short temporary perturbation is commonly encountered in many evolutionary processes, such as neural networks, artificial intelligence, robotics, communications systems and biological systems and so on. Impulsive differential systems provide a natural description of these phenomena of several real world problems. On the other hand, it can't be separeted from the effects of stochastic environment on the development of a dynamical system. So it is great significance to study stochastic impulsive systems. Hybrid dynamical systems have been applied extensively such as the control of mechanical, the automotive industry, flight and air traffic control, intelligent vehicle highway systems, etc. The both of Markov jumping systems and switched systems are special classes of hybrid system. So it is needed to study the stability and control problems for stochastic impulsive systems with Markovian jumping and impulsive switched systems.In this thesis, the control problems of stochastic impulsive system and impulsive switched system are studied. The main work of this thesis lies in the following:1. Robust stability and H_∞control for uncertain linear impulsive stochastic systems are investigated. Three classes of impulsive control systems are considered: the systems with stable/stabilizable continuous-time dynamical subsystems and unstable/unstabilizable discrete-time dynamical subsystems, the systems with unstable/unstabilizable continuous dynamical subsystems and stable/stabilizable discrete-time dynamical subsystems, and the systems that both the continuous-time dynamical subsystems and the discrete-time dynamical subsystems are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for three classes of impulse control systems are derived in terms of an average dwell-time condition and linear matrix inequalities, the design of a robust H_∞controller for each system is presented.2. p—moment exponential stability and almost sure exponential stability for nonlinear impulsive stochastic systems with Markovian jumping are studied. Based on Lyapunov functions and the concept of average dwell time, sufficient conditions for exponential sta- bility are established. The algebraic criterion for exponential stability is derived in terms of an average dwell-time condition and M—matrix.3. Input-to-state stability of nonlinear impulsive switched systems with unstable subsystems is investigated. Sufficient conditions on Input-to-state stability for switched systems with impulsive and without impulsive are derived in terms of an average dwell-time and designing the switching law.Numerical examples are provided to demonstrate the effectiveness and applicability of proposed approach.