Analysis And Synthesis Of Markov Jump Systems Subject To Actuator Saturation

Markov jump linear systems (MJLS),which comprise a new field of complex systems modeling and the research of control theory, are introduced for the strong engineering background. Various practical systems such as manufacturing systems, biology and chemistry systems, electric power systems as well as economic systems, which subject to sudden environment changes, changes in the interconnections of subsystems, modification of the operating point of a linearized model of a nonlinear system, random failures and repairs of the components and so on, involve both time-evolving and event-driven mechanisms. MJLS are a special class of hybrid systems with two components in their state vector: the modes and the states. The mode is described by a continuous Markovian process with a finite state space. The state in each mode is represented by a system of differential equations.Saturation is probably the most commonly encountered nonlinearity in the real-world process industries, if the controller is designed without considering the saturation, then when the states go into the area of saturation, the stability of the closed-loop controlled system can not be assured. Generally, the stability of the whole systems with actuator saturation can not be guaranteed,therefore, the domain of attraction of the systems is only one part of the state space.As the exact domain of attraction is hard to be achieved, it is always estimated by means of invariant ellipsoid. In this thesis, based on the stochastic Lyapunov function, linear matrix inequality approach is adopted to investigate the analysis and synthesis of Markov jump systems subject to actuator saturation.The major contributions of this thesis are as follows:1. For a class of uncertain Markov linear jump systems subject to actuator saturation, the stochastic stability analysis is discussed and then the estimation of domain of attraction is given. Considering the exogenous disturbance of systems, L 2gain is used to analyze the disturbance attenuation ability. Optimization problems in the form of LMIs are used to optimize L 2gain, and the controller obtained can minimize the bound of L 2gain.2. The stochastic stabilization problem for a class of Markov jump systems subject to actuator saturation is considered. The problem is solved by static output feedback, observer-based output feedback and dynamic output feedback respectively. The gains of output feedback controllers are mode-dependent and governed by the stochastic transition rate matrix. The concept of domain of attraction in mean square sense is used to analyze the stochastic stability, and sufficient conditions which guarantee the intersection of ellipsoid invariant set under different modes in the domain of attraction are presented. Furthermore, convex optimization problems with LMI constraints are formulated to design the output feedback controllers such that the estimated domain of attraction which contain the given initial states are maximized.3. A robust model predictive controller design method is proposed for a class of uncertain discrete-time Markov jump systems subject to actuator saturation. In terms of the engineering application, the uncertainties are considered to exist in system parameters and jumping transition probabilities, both of which are assumed to belong to some convex sets. The predictive controller is obtained by minimizing a worst-case infinite horizon objective function at each sampling time and the predictive control sequence is presented as a saturated state feedback control law at each step. The resulting closed-loop system is mean square stable and the proposed controller is obtained using semidefinite programming which can be easily solved by means of LMIs.4. For a class of bilinear stochastic discrete-time systems with Markov jump parameters subject to actuator saturation, the stochastic stability is respectively investigated by using general quadratic Lyapunov function and saturation-dependent Lyapunov function. A set of mode-dependent ellipsoid invariant sets is introduced to construct the stochastic stability region. Two design methods of saturation controller are presented, which dependent on the mode transition rate matrix. Then, the problem of robust guaranteed cost control for a class of continuous uncertain bilinear stochastic systems with Markov jump parameters subject to actuator saturation is discussed. All the results are provided in the form of linear matrix inequality.The conclusion and perspective are given in the end of the thesis.