Research On Theory And Application Of Stability Of Switched Systems

The switched systems(SSs)is a special hybrid system(HS)consisting of a series of continuous or discrete subsystems and switching rules that coordinate these subsystems.With the frequent appearance of SSs in various engineering applications,the research of SSs has attracted more and more scholars' attention.For the actual system,stability is a prerequisite for its normal work and operation.Therefore,the research on the stability of SSs is of great theoretical and practical significance.Nowadays,research on SSs mainly focuses on the stability of system.However,when delay and switching exist in a system at the same time,the system becomes complex.Time delay is also an important reason to affect the stability change of SSs.In addition,the uncertainty of the system caused by external interference input,measurement error,parameter estimation error and so on all have a great influence on the stability of the system.Therefore,it is of great significance to consider the influence of these factors when studying the stability of SSs.Although many theories and methods have been proposed for the stability analysis of SSs,there are still some shortcomings and areas for improvement in these theories and methods.On the basis of summing up the previous work,the thesis studies the stability analysis of several kinds of continuous time and discrete time SSs.Based on SSs theory and the Lyapunov function approach,sufficient conditions of the stability of SSs are obtained in the form of linear matrix inequality(LMI).The obtained conditions can be solved directly by using the LMI Toolbox in MATLAB.Finally,the validity of the proposed conclusion is verified by numerical examples.There are several aspects to the main work:1.The state estimation problem of a class of Markov jumping neural networks(NN)with two additive delay is studied.By constructing a Lyapunov functional with multiple integral items and using the improved integral inequality,the conditions are obtained to guarantee the global stability in the mean square sense of the system with parameter uncertainty or no parameter uncertainty.2.The extended dissipation state estimation problem of a class of uncertain discrete time Markov jump NN with finite segmented homogeneous Markov chain and mixed time delay is studied.By constructing a suitable Lyapunov functional and designing Markov switching estimator,the sufficient conditions for extended dissipation of the system in the two cases of all known and partially known elements in transition probabilities matrix are obtained.3.The distributed state estimation problem of a class of sensor networks(SNs)with stochastic switching topologies is studied.In SNs,we consider a redundant channel.By designing the distributed state estimator to estimate the state of the target object,the sufficient conditions for the global asymptotic stability of SNs in the mean square in the case of stochastic variation nonlinearity,stochastic disturbance and measurement loss are obtained.4.The problem of exponential stability in mean square sense and reliable data sampling controller design of a class of nonlinear SSs is studied.In SSs,a hybrid actuator fault model is used to describe the nonlinear problems encountered in controller design,and the influence of data packet loss and multiple sampling periods on the system is considered.Then,by using the input delay approach and Average Dwell-time approach,the sufficient conditions to ensure the exponential stability in the mean square sense of the system and satisty the performance index are given in the form of LMI.5.The stochastic synchronization problem of a class of semi-Markov jumps chaotic lur'e systems is studied.Firstly,the original system is transformed into a stochastic timedelay system by using the input delay approach.Secondly,by maximizing the use of the available information in the actual sampling mode,the probability distribution values of the stochastic delay taking in 8)given intervals can be obtained.Then,a newly augmented Lyapunov functional is constructed.Based on that,the sufficient conditions for stochastic synchronization between the master system and the slave system are obtained.