Stability Analysis For A Class Of Linear Impulsive Switched Systems

As one of the most important classes of the hybrid dynamic systems,the switched system not only has important scientific value in the teoretical research,but also has a wide range of applications in practical engineering.In the real life,the swithed system is easily influenced by the outside world at certain time moments,resulting in state jumps,which generates the impulsive switched system.Compared with the general switched sys-tem,the impulsive switched system has the characteristics of both the switched system and the impulsive system,which makes the stability analysis of the impulsive switched system much more complicated.In recent years,the impulsive switched system has at-tracted the attention of many researchers.So far,although some valuable research results have been obtained for the impulsive switched system,there are still many problems that need to be further solved.Based on the existing research results,this paper will further study the stability analysis of the impulsive switched system.The main contents are as follows:Chapter 1 is the introduction.We summarize the research significance,methods and existing achievements of the switched system,the switched singular system,the impulsive switched system and the impulsive switched singular system.In chapter 2,we investigate the exponential stability problem of the impulsive switehed singular system under any switching signal based on dewell-time specifieations with nonlin-ear uncertainties by constructing the multiple time-varying Lyapunov function method,which obtains the sufficient conditions ensuring the exponential stability of such systems,the nonlinear uncertainties meet with corresponding Lipschitz conditions.Firstly,when the dwell-time is confined by a pair of upper and lower bounds,the conclusions ensur-ing the E-exponential stability of impulsive switched singular systems are proposed by constructing,the multiple time-varying Lyapunov function methods.Secondly,in consid-eration of singular system,we decompose the original singular matrix into a non-singular reduced order matrix and an algebraic constraint inequality,thus we use the obtained E-exponential stability conclusion of the inpulsive switched singular system to solve its('xponential stability problems.At the same,unlike the classical dwell-time method.the dwell-time is given in advance,which is not calculated by Lyapunov functions of the subsystems.The proposed conditions can be formulated as the solutions on linear matrix inequality problems.Finally,an example is presented to demonstrate te the effectiveness of the proposed method.In chapter 3,we investigate the stability analysis of the impulsive switched system under any switching signal based on dwell-time specifieations with time-delay and uncer-tainties by constructing the multiple time-varying Lyapunov functional method,which obtains the sufficient conditions ensuring the global asymptotic stability of such systems.The system is under consideration of time-delay,parameter uncertainties and nonlinear uncertainties.The parameter uncertainties are norm-bounded time-varying uncertain-ties which enter all the state matrices,the nonlinear uncertainties meet with the linear growth condition.Firstly,owing to the existence of state delay,so we consider the multi-ple time-varying Lyapunov functional in two aspects.Secondly,mltiplying both sides of the matrix inequality by the appropriate diagonal matrix.At the same time,covert it to the form of the linear matrix inequality by Schur complement lemma.The proposed con-ditions can be formulated as the solutions on linear matrix inequality problems.Thirdly,the switching signal which guarantees the global asymptotic stability of the system is de-signed.Finally,an example is presented to demonstrate the effectiveness of the proposed method.In chapter 4,we summarize the main research contents and perspective end the dissertation.