Research On Input-to-State Stability And Observers Of Impulsive Systems

Systems with impulses have some common characters of continuous systems and discrete systems.Impulsive systems have some background from practice,related research results are valuable for applications.In recent years,the topic concerning input-to-state stability and the topic concerning the design of the observers of impulsive systems have attracted the attentions from lots of researchers,with the process of the research conducted by the researchers,many meaningful results have be established,the applications of the related results have been founded in many fields such as control theory,biological mathematics and some physics application subjects.For an impulsive system,when considering the affect from the outside of the system,some kind of stability should be considered,and the problem of how to realize this kind of stability are interesting.In this kind of problems,the so called input-to-state stability is one of the most famous concepts.The results concerning the input-to-state stability of impulsive systems are fruitful.However,it is noted that those impulses are happed at some instants,that is the instantaneous impulses.While in some applications,the impulses happened at some instants and hold on for a tiny time length,this is the so called non-instantaneous impulse.This kind of impulses have some important background.The first point of this thesis is concerning the input-to-state stability of the systems with non-instantaneous impulses.By using the Lyapunov function with indefinite derivatives and the average dwell on condition on the impulse,we get a sufficient condition to assure the input-to-state stability of the system.In the end,we use an example to show the efficiency of the theorem.Because of the complex of impulsive systems,it is often very difficult to know the their states totally.By designing some kind of observers for the system and then using the observer to study the state of the original system is an efficient methods.The second point of this thesis is concerning the design of an observer for an impulsive system.Using the average dwell time condition to the impulse sequence and the linear matrix inequality,we design an observer,then we show the efficiency by an example.In the last chapter,we give a conclusion of the results of this thesis,and then we proposed some interesting topics to be done in the future.