Finite-Time Control Of Discrete-Time Semi-Markov Jump Systems

There is such a kind of stochastic switching system in industrial process that system faults or environmental change will trigger the abrupt variations of structure and parameter.Researchers need cope adequately with the abrupt phenomena which may change the normal operation of the system,by using the statistical information on the rate at which these events take place,therefore,the researches on the control of stochastic systems have become one of the hot issues in recent years.Markov jump systems are common form of stochastic switching system,its dynamical processes involved with stochastic switching subject to a Markov process,which indicates the change of model is probability-dependent.However,the application of Markov jump systems is restricted by that the sojourn-time of each subsystem is subject to exponential distribution(geometric distribution in discrete-time domain),the sojourn-time of semi-Markov jump systems(S-MJSs)can be subject to arbitrary probability distribution,which makes S-MJSs have a wider application.In addition,for systems with overshoot or settling time restriction,it is of great significance to study their dynamic performance in a limited time range.Different from the asymptotically stability which requires that the system state converge to equilibrium point,finite-time stability can limit the amplitude of the system state trajectory in a certain time range,make the system dynamic performance meet the control index,and solve the problem of excessive system state fluctuations,therefore,it has high research value.For discrete-time S-MJSs,this thesis limits the sojourn-time of each system mode,employs Lyapunov function theory and semi-Markov kernel method to study the finite-time control prob-lem of the system,gives sufficient conditions for finite-time stability of discrete-time S-MJSs,and designs robust H_∞controller guarantee system to be finite-time bounded with given H_∞performance.On this basis,the finite-time boundedness of discrete-time S-MJSs with incom-plete transition information is discussed.The main research content consists of the following three parts:(1)The problem of finite-time control for a class of discrete-time S-MJSs is studied.The upper and lower bound of sojourn-time are considered simultaneously,which gives the concept ofσ-error finite-time stability and guarantees the corresponding criteria based on semi-Markov kernel to be numerically testable.The method of the maximum number of jumps is proposed for the finite-time analysis of stochastic switching system.On the basis of proposed σ-error finite-time stability criteria,the corresponding design method of mode-dependent state-feedback control law is given to guarantee the closed-loop system to be finite-time stability.(2)The finite-time robust H_∞ control problem for a class of uncertain discrete-time S-MJSs is addressed.The Lyapunov function inequality between current mode’s end point and next mode’s begin point is obtained by using the semi-Markov kernel method,so that the new criterion can solve the finite-time boundedness problem.Proposing the mode-dependent sojourn-time mathematical expectation approach to estimate the numbers of times of each mode being activated under the overall system running time,so that the proposed finite-time bounded criterion is less conservative than the previous theory.On this basis,the H_∞performance is analyzed and the corresponding design method of mode-dependent state-feedback control law is given to guarantee the corresponding closed-loop system to be finite-time bounded with given H_∞performance.(3)The finite-time control problem for a class of discrete-time S-MJSs with limited information access is investigated.Considering that the sojourn-time and transition probability informa-tion of discrete-time S-MJSs are partially known,the mathematical expectation formula of sojourn-time and the Lyapunov function value inequality between current mode’s end point and next mode’s begin point are reconstructed,the finite-time boundedness criterion with limited information access is established,and the finite-time controller is designed to guar-antee the finite-time boundedness of the closed-loop system.