Research On Stability And Control Of Impulsive Systems

Impulsive dynamic system is a special hybrid system.Due to its wide application prospects,more and more scholars have paid attention in recent years.Due to the inherent characteristics of the impulsive system model,the state trajectory of the system will jump,which makes the problems faced in the research process more complex and changeable.In this paper,the stability and controller design of linear impulsive system and nonlinear impulsive system are studied separately,mainly including the following contents:First,the stability and control synthesis of linear impulsive systems are discussed.The linear impulsive system studied in this paper has a piecewise linear jump map,and time regularization is embedded in the system.An extended Lyapunov-like function is used to analyze the stability of linear impulsive systems.The special feature of this type of power function is that it allows the value of the function to increase at a bounded growth rate within a certain time interval,and passes in each transition instantaneously reducing function values to compensate for the increased amount.Based on this extended Lyapunov-like function,this paper presents sufficient conditions for the global asymptotic stability of the linear impulsive system studied.According to the obtained stability conclusion,the design method of linear feedback controller that can stabilize the linear impulsive system is further deduced.Then,calculation examples and simulation results are given to verify the validity of the proposed conclusions.Secondly,the stability analysis method of nonlinear impulsive system is studied.By considering the nonlinear continuous system and the nonlinear continuous comparison system,the comparison theorem of the nonlinear continuous system is introduced and gradually extended to the nonlinear impulsive system.On this basis,by introducing vector Lyapunov function,a sufficient condition for the stability of the nonlinear impulsive system is obtained according to the comparison theorem.Under the condition that the vector Lyapunov function satisfies certain differential inequalities,the theorem is given to prove that the stability of the comparative impulsive system means the stability of the original impulsive system.Finally,the controller design method of the nonlinear impulsive system is studied.This paper introduces a control vector Lyapunov function for nonlinear impulsive systems.The existence of this control vector Lyapunov function means the existence of a pair of state feedback controllers that can stabilize the system.According to the definition of the control vector Lyapunov function,the design method of the state feedback controller is given.Furthermore,this paper studies a special structure of nonlinear impulsive system,and gives the specific design of the controller of this special structure of impulsive system.Then,related calculation examples are given,and the simulation results verify the correctness of the conclusions presented in this paper.