| During the operation of the actual control system,the system may suffer from hardware failure,sudden changes in environmental conditions,changes in the connection between multiple subsystems,etc.As a special kind of stochastic systems,Markov Jump Systems(MJSs)can be used to describe this kind of special and complex phenomena.Singular Markov jump systems(SMJSs)are a combination of singular systems and MJSs,which are more typical hybrid systems with wider applicability than ordinary state space systems and can describe more physical properties of the system as well as other characteristics,and are widely used in power systems,chemical systems,etc.On the other hand,Lyapunov stability theory is preferred for the stability analysis of SMJSs,which is more concerned with the asymptotic stability of the system in the infinite time domain and reflects the steady-state performance of the system.However,in practical engineering applications,such as rocket launch and robot control,it is more concerned with the system state in the finite time domain.Compared with Lyapunov stability,finite-time stability can reflect the transient performance of the system in the finite time domain,which makes the finite-time control problem of SMJSs have important theoretical significance and application value.For discrete time SMJSs,the problem of finite-time control for discrete-time SMJSs is studied based on the theory of Lyapunov functions and the theory related to stochastic systems,and the linear matrix inequality is used as a proof tool to give sufficient conditions for the finitetime stability and boundedness of the closed-loop system,and a design method for the controller in different cases is given.The main research is divided into three parts as follows:Firstly,the finite-time control problem of discrete-time SMJSs with time-varying delay is studied.Considering the case where the transfer probabilities are completely known,the design of a state feedback controller is given by designing a new suitable class of Lyapunov functions that give sufficient conditions for the regular,causal and finite-time stability of the system in the form of strict delay-dependent linear matrix inequalities.Then,the controller is designed so that the closed-loop system is regular,causal,and finite-time stable by considering the case where the transfer probability is partially known,and the nonlinear terms in the matrix inequality are handled by matrix transformation.Then,the problem of finite-time asynchronous control for discrete-time SMJSs based on event-triggered is investigated.To improve the utilization of network resources,an eventtriggered mechanism is employed to convert the closed-loop system into special SMJSs with time-varying delay.Meanwhile,a Hidden Markov Model is developed to explain the asynchronous phenomenon between the controller mode and the system mode.The method of Lyapunov functions is applied to give sufficient conditions for the closed-loop system to be regular,causal and finite-time bounded and to satisfy the H∞ performance index by constructing suitable Lyapunov-Krasovskii generalized functions with the help of Jensen inequality and the free power matrix.The design method of the state feedback asynchronous controller is given by matrix construction and matrix transformation to deal with the nonlinear terms in the conditions.Finally,the problem of static output feedback finite-time control for discrete-time SMJSs based on event-triggered is investigated.The closed-loop system model under static output feedback is established by considering the event-triggered mechanism of signal transmission and network transmission delay.Applying the method of Lyapunov functions,sufficient conditions for the closed-loop system to be regular,causal and finite-time bounded and to satisfy the H∞performance index are given by constructing a suitable Lyapunov-Krasovskii general function.A design method for the static output feedback control gain matrix is given based on matrix decomposition and variable separation. |
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