Stability Analysis Of Nonlinear Stochastic Impulsive And Switched Systems

As two special classes of hybrid systems,impulsive systems and switched systems have attracted considerable attention in recent years due to their numerous interdisci-plinary applications in different fields of science and engineering.Impulsive systems model real world processes that undergo abrupt changes(impulses)in the state at dis-crete times;switched systems model practical systems whose dynamics are chosen from a family of subsystems based on a switching law.Many physical systems can be mod-eled as impulsive/switched systems,such as networked control systems,multi-agent systems,neural networks,mechanical systems.In the literature,there are numerous works on impulsive systems or switched systems,and many salient results can be found on stability analysis of impulsive/switched systems.In physical systems,external dis-turbances are inevitable.Both the continuous dynamics and discrete dynamics may be affected.If the control systems are subjected to random noises,then stochastic sys-tem modelling is required.On the other hand,time delays are frequently encountered in many engineering systems,and may induce oscillation,instability and poor perfor-mances.These external disturbances and time delays result in more complex system models and their effects on system stability deserve further study.In this dissertation,based on the characterization of hybrid systems,we study sta-bility and stabilization of stochastic switched systems,stability analysis of stochastic impulsive systems,and further stability analysis stochastic impulsive switched(time-delay)systems.The main contributions of this dissertation are as follows:· We study stability of stochastic impulsive systems using general Lyapunov func-tions and fixed dwell-time condition.For both the stable continuous dynamic-s case and the stable discrete dynamics case,sufficient stability conditions are established.Moreover,the relationship between fixed dwell-time and average dwell-time is discussed.Finally,two numerical examples are given to illustrate the developed results.· We study stability and stabilization of stochastic switched systems with asyn-chronous switching.First,according to the different reasons for the asynchronous switching phenomena,the asynchronous switching is divided into two types:time-delay switching and unmatched switching.For such two types of asyn-chronous switches,stability conditions are derived for stochastic nonlinear switched systems,switched controllers are designed for stochastic linear switched systems.Finally,a numerical example is presented to show efficientness of the obtained results.· Based on the above study,we further consider stability of stochastic impulsive switched systems.Using multiple general Lyapunov function and fixed dwell-time,sufficient conditions are obtained to guarantee system stability.This work extends the results for stochastic impulsive systems to the stochastic impulsive switched system case.At last,two numerical examples from neural networks and networked control systems are used to demonstrate the established results.· Furthermore,we study stability of stochastic impulsive switched time-delay sys-tems.Instead of scalar Lyapunov function approach,the vector Lyapunov func-tion approach is applied,which has many advantages over the scalar Lyapunov function approach in term of the construction of Lyapunov function and stability analysis.In addition,we also consider the relationships among the vector Lya-punov function method,the scalar Lyapunov function method and the method based on comparison principle.Finally,we present two numerical examples to show the advantages of the obtained results.· According to the mechanism of impulses and switching,we study quantized feed-back stabilization problem of nonlinear systems.First,the effects of quantiza-tion mechanism on the system state are studied,and then a switched controller is proposed.Using such a switched controller,quantized feedback stabilization is addressed for the following three quantization cases:state quantization,input quantization and output quantization.