Robust And Sliding Mode Control Of Markov Jump Systems

Markov(or Markovian) jump systems (MJS for short) is one kind of hybrid systems. The analysis and controller designing for MJS have been widely concerned recently. MJS is usually used to model systems that suffering random abrupt changes in their parameters or components. In such systems there exist more than one working modes among which the system works. The changing from one mode to another follows a Markov process. When the system working in each mode, it could be modeled by a determinist system, and the whole system jump among such determinist systems. Due to it jumps following some probability, so we are not able to use the existed theory and research results of determinist systems to such Markov jump systems directly. Because of the complicated information of MJS itself, the research method for such systems is very different from the traditional systems, which is governed by single time or event system. On another hand, in practice a large number of systems exist Markov jump phenomenon, so, the study of MJS has a profound theoretical and practical value.This dissertation focuses on state-feedback and output-feedback controller design for several classes of Markov jump systems. By using the method of robust H∞control, sliding mode control theory, the linear matrix inequality and some important inequalities, the stabilizing state-feedback controllers and the output-feedback controllers are designed respectively, and the detailed design procedures of controllers are provided. In addition, by means of stochastically stable theory of Markov jump systems, the corresponding sta-bility analysis are given. Numerical examples and simulations illustrate the advantages and effectiveness of the proposed approaches. The main contents of this dissertation are composed of the following five parts:Firstly, for a class of discrete-time Markov jump systems, which subject to polytopic-type parameter uncertainty in the matrices of the system state-space model, the problem of robust H∞output-feedback stabilization is investigated. Considering that there not exists the disturbance in the system, a static output feedback controller is designed to ensure that the closed-loop system is mean square stable. An LMI formed sufficient condition is given to guarantee the existence of such a controller. Considering the system suffering disturbance, an H∞performance function is established, and a sufficient condition of the existence of an output feedback controller, under which the underly system is mean square stabilized and with some level of H∞performance, is given. The efficiency of the output-feedback controller is demonstrated by a simulation example.Secondly, for a class of discrete-time Markov jump systems, in which the transition probability matrix is partly known, the problem of dynamic output feedbackH∞control is developed. Sufficient conditions are proposed to guarantee the stochastic stability of the underlying system through using several linear matrix inequity. The system is not only stabilized under the designed output feedback controller but also with a7performance. Numerical examples are given to show the potential of the proposed techniques.Thirdly, for a class of discrete-time Markov jump systems that subject to actuator saturation, the problem of output-feedback stochastic stabilization is investigated. The concept of domain of attraction in mean square sense is used to analyze the closed-loop stability. Considering that there not exist disturbance in the system, a mode-dependent static output feedback controller is developed, and a sufficient condition is given to en-sure that the closed-loop is mean square stabilized under such a controller. Considering the system suffering disturbance, an H∞performance function is established, and a suffi-cient condition of the existence of an output feedback controller, under which the underly system is mean square stabilized and with some level of H∞performance. The efficiency of the control scheme is demonstrated by a simulation example.Fourthly, the problem of state feedback and output feedback sliding mode control for a class of discrete-time Markov jump systems is considered. The uncertainty of the system is considered as a function of the system inputs, states and time and satisfying the matched condition. A sufficient condition is provided to guarantee the existence of the discrete-time sliding modes by LMI form, and a sliding mode control law is designed to make the system states reach to the designed sliding mode and keep on it stochastically stable. Considering that the system states are not completely known, a static output feedback controller is designed. The system is stochastically stabilized by such a controller. The efficiency of the state-feedback controller is demonstrated by a simulation example.Fifthly, the problem of sliding mode output feedback for a class of continue-time Markov jump systems with some unmeasured states is investigated. An observer is de-signed to estimate the system states, and a sliding mode controller is synthesized for driving the system to reach to and maintain on the sliding mode, which is designed on an integral function. Sufficient conditions for the existence of the controller under which the underlying system are stochastically stabilized are derived via LMIs. And the parame-ters of the controller could be calculated from the LMIs condition. A numerical example shows the validity and potential of the developed results.Finally, the results of the dissertation are summarized and further research topics are pointed out.