Stability Of Nonlinear Systems Involving Impulses

In the past two decades,event-triggered control has been widely applied in the fields of control science,such as general nonlinear systems,neural network systems,multi-agent systems,hybrid systems,and so on.The event-triggered mechanism can avoid unnecessary waste of computing and communication resources caused by time sampling mechanism.Thus it can save a lot of resources to extend the life of the system in practice.In recent years,the problems related to event-triggered control have received a lot of academic attention and have become a hot issue in control theory research.In this thesis,we focus on the stability of nonlinear systems with impulsive effects,using event-triggered control methods,where both event-triggered conditions and controllers are required to be designed.The outline of the rest of this thesis is as follows:In Chapter 1,we introduce the academic background and significance of the research topic,the main research work of this thesis,and the definitions and theorems that need to be used.In Chapter 2,we investigate two types of nonlinear systems with a single impulse(impulsive control and impulsive disturbance).First,we present the basic results of event-triggered state feedback sampling control based on Lyapunov stability theory,where we consider that the system is sampled with sampling errors which approximates the impulse effect.Using the Lyapunov method,sufficient conditions are given to ensure the exponential stability(ES)of the system.We use the linear matrix inequality(LMI)for the event-triggered mechanism and controller design.Moreover,our results effectively exclude the Zeno phenomenon.After that,we consider a hybrid control combining sampling and impulsive control to study the exponential stability results of the nonlinear system,where we will involve the co-design of the sampling controller,the impulse controller and the event-triggered mechanism.In Chapter 3,we apply an event-triggered control strategy to study the global exponential stabilization of a nonlinear system under the effect of mixed impulses.Two types of impulses(i.e.,stabilized and destabilized)can coexist in the full control process,and the events and impulses can occur at different times.Inspired by the average dwell time(ADT)method,the limit conditions of impulses are given,sufficient conditions for system stability are obtained,and two corollaries on the single impulse effect are obtained.In addition,the design of the event-triggered mechanism and the control gain are solved by using the LMI method.In Chapter 4,we utilize output-based event-triggered control to deal with the global exponential stability of nonlinear impulsive systems.In this chapter,we consider two event-triggered mechanisms separately.First,under the static event-triggered mechanism,the Zeno phenomenon is excluded and a sufficient condition for the global exponential stability of the system is derived.Then,based on the static triggering mechanism,we introduce dynamic variables to obtain the dynamic event-triggered mechanism and obtain sufficient conditions to ensure the stability of the system under the dynamic event-triggered mechanism,and we can see that the dynamic triggering mechanism has the advantage of further reducing the number of triggering compared with the static triggering mechanism.