Finite-time Control And Filtering Of Singular Semi-markov Jump Systems

Due to abrupt changes in environmental conditions,devices failures,and operating points,some-times,the structure and parame-ters of the practical dynamics may be changed.As a kind of hybrid systems,Markov jump systems(MJSs)can be used to model this stochastic situation.Compared with MJSs,semi-Markov jump systems(SMJSs)obey not only the exponential distribution,but also the Gaussian distribution,Weibull distribution and other more general dis-tributions,which have a wider application in practical situations.In addition,singular systems can be decomposed to fast subsystems depicted by algebraic equations and slow subsystems depicted by differential equations or difference equations,and also play an important role in practical application.Singular systems are more general than the normal state space systems,so it can describe the more complicated system,such as electric power system and economic system,e-tc.Singular semi-Markov jump systems(SSMJSs)can describe actual systems more accurately.With the development of singular systems and SMJSs,the analysis and synthesis of SSMJSs have been paid more and more attention.Besides,stability analysis is an impor-tant issue in system research.Generally,there are many studies on Lyapunov stability.In this case,Lyapunov function or Lyapunov-Krasovskii functional is usually constructed to de-termine whe-ther it is asymptotically stable by its derivative.In this case,the state of the system over an infinite-time interval is concerned,which reflects the steady-state performance of the system.However,in practical applications,such as missile systems and robot systems,the transient performance of the system needs to be concerned,that is,the state of the system in a predefined time interval.In this thesis,the finite-time control and filtering problems of SSMJSs are studied by stochastic system theory and Lyapunov function theory.Sufficient conditions of finite-time stability and boundedness for closed-loop systems are given,and controllers and filters are de-signed.The main research content is divided into the following three parts:Firstly,the finite-time state feedback control problem of SSMJSs is studied.By using the me-thod of Lyapunov function and constructing suitable Lyapunov-like function,sufficient conditions of regularity,absence of impulse and finite-time stability for the closed-loop system are given,and the gain matrix of the controller is obtained.Then,considering the disturbance with finite amplitude,the controller is designed in the same way so that the closed-loop system is regular,impulse-free and finite-time bounded.The semi-Markov jump coupling terms are dealt with by matrix transformation,and the equality conditions which are difficult to solve in the conditions are transformed into linear matrix inequalities by decomposing matrices and constructing new matrices.The validity of the conditions is proved by numerical simulation.Then,the finite-time control problem of event-triggered SSMJSs is studied.By defining some new functions,the ne-twork-induced time delay in discre-te event-triggered scheme is mod-eled into the time delay of the system.Therefore,this problem is transformed into the finite-time control problem of the SSMJS with time-varying delay,but it should be noted that the derivative of the time-varying delay is different from that of the normal time-varying delay system.By constructing a suitable Lyapunov-Krasovskii functional,using Jensen inequality and Wirtinger inequality,sufficient conditions of regularity,absence of impulse and finite-time boundedness for closed-loop systems are given.Similarly,equality conditions and coupling terms in condi-tions can be addressed through matrix construction and decomposition.An example is presented to demonstrate the effectiveness of the proposed me-thod.Finally,the asynchronous finite-time H_∞filtering problem of SSMJSs is studied.For the asynchronous phenomenon be-tween the mode of the system and the filter,a hidden Markov model is introduced to deal with it.By constructing a suitable Lyapunov function based on the me-thod of Lyapunov function,sufficient conditions are given to guarantee that the filtering er-ror system is regular,impulse-free and finite-time bounded,and with desired H_∞performance.Furthermore,appropriate matrix with special structure and slack matrix are introduced to deal with the coupling be-tween system matrix and Lyapunov function matrix.Therefore,some con-straints of Lyapunov function matrix are eliminated,which implies that the desired filter can be designed,and the parame-ter matrix of filter can be obtained.The validity of the criterion is verified by numerical examples.