Stability Analysis And Control Of Linear Impulsive Switching System

Due to the needs of social development and scientific and technological progress,people have more and more extensive research on the system,and the research on the system is more and more complex and in-depth.As two kinds of hybrid systems,impulsive system and switching system have their own properties.Many practical problems can be solved by using these system models.For example,the ideal results can be obtained by applying control to some systems that do not reach the expected results.Therefore,it is necessary and meaningful to study and analyze these systems.In this paper,the stability of the system is studied,and some systems are controlled.The main contents include the following aspects:Firstly,the stability of the impulsive system is studied.By studying the properties of the system,the expression of the system is given,and the two schemes are selected according to the logic judgment at the pulse time.The sufficient conditions for the asymptotic stability of linear impulsive system based on logical judgment are obtained.In order to verify the validity of the conclusion,the method of constructing comparative system is used to prove the conclusion,and then a numerical example is given and simulated.Secondly,this paper studies the stability of switched systems,obtains the conditions of system stability by similar methods,and verifies them.Then,this paper studies the relatively complex impulsive switching system,which is the extension and synthesis of impulsive system and switching system.Combined with the previous research,the sufficient conditions for the stability of the system are obtained through analysis.Then,the conclusion is verified by using the definition and lemma,and the conclusion is correct.Finally,the state feedback control is applied to those systems which do not meet the stability conditions.It is to design a reasonable state feedback controller to make the system stable,and the theoretical criteria are given to prove the feasibility of the state feedback controller design,and numerical examples and inverted pendulum system examples are given to verify the correctness of the conclusion by system simulation.