Input-to-state Stability Analysis Of Impulsive Stochastic Nonlinear Systems

As one of the basic characteristics of control systems,stability has become an important research content in the field of international systems and control.The stability research of the control system involves Lyapunov stability,computer science and technology,matrix theory,chaotic secure communication and other disciplines,and its related achievements have been widely used in communication systems,bioengineering,financial mathematics and other fields.In the process of studying the stability of the control system,it is often accompanied by the influence of factors such as random noise and time delay.Therefore,the research on the stability of nonlinear control systems affected by factors such as time delay and random noise has also become a hot research topic.The input-to-state stability(ISS)was first proposed by Sontag,it shows that if a system is input-to-state stability,no matter what its initial size is,under the action of external bounded input,its system will eventually reach a stable state and its final state will only be the input size is related and changes in direct proportion to the input size.The proposal of this theory also provides a strong basis for the stability study of the control system.Because uncertainty is the most important factor affecting the complexity of control system,in order to better study the performance of the system,the research on the input-to-state stability of impulsive stochastic systems has also become a hot spot in today's academic circles.Based on the above analysis,this paper mainly studies the input-to-state stability of impulsive stochastic nonlinear systems.The main work includes the following two aspects:(1)The input-to-state stability,stochastic input-to-state stability(SISS)and integral input-to-state stability(IISS)of impulsive stochastic nonlinear systems with indefinite Lyapunov derivatives are studied.Considering the general impulsive stochastic nonlinear system,the sufficient conditions of the system input-to-state stability,stochastic inputto-state stability and integral input-to-state stability are obtained under the condition of uncertainty of the derivative of Lyapunov function by using Lyapunov stability theory and mean dwell time(ADT)methods.On this basis,the input-to-state stability and the integral input-to-state stability of impulsive stochastic system with multiple jump mapping are studied.Finally,the validity of the theoretical results is verified by numerical simulation.(2)The integral input-to-state stability of impulsive stochastic systems with time delay is considered.By using Lyapunov stability theory and integral input-to-state stability theory,the integral input-to-state stability of general impulsive stochastic nonlinear systems with time delay is studied under the condition of fixed delay impulses.The integral input-to-state stability of systems with some subsystems and impulsive stochastic nonlinear systems with multiple jumps are studied.Finally,a numerical example is given to verify the effectiveness of the theoretical results.