| Switched systems form a class of hybrid systems consisting of a family of subsystems described by continuous-time or discrete-time dynamics, and a rule specifying the switching among them. Switched systems have received increasing attentions in the past few years, since many real-world systems such as chemical processes, transportation systems, computer-controlled systems, and communica-tion industries can be modelled as switched systems. More importantly, many intelligent control strategies are designed based on the idea of controllers switching to overcome the shortcoming of the traditionally used single controller and to improve the performance, thus making the corresponding closed-loop sys-tems to become switched systems. On the other hand, sliding mode control (SMC) has proven to be an effective robust control strategy for incompletely modelled or nonlinear systems since its appearance in the 1950s. In the past two decades, sliding mode control has successfully been applied to a wide variety of practical engineering systems such as robot manipulators, aircrafts, underwater vehicles, spacecrafts, flexible space structures, electrical motors, power systems, and automotive engines. Sliding mode control utilizes a discontinuous control to force the system state trajectories to some predefined sliding surfaces on which the system has desired properties such as stability, disturbance rejection capabil-ity, and tracking ability. Many important results have been reported for this kind of control strategy, which includs some different systems, such as uncertain sys-tems, time-delay systems, and stochastic systems.The main contents can be stated as follows:1. In Chapter 1, we first present the background, the basic conceptions, and some related approaches for the switched systems. Then, we sum-marize and analyze the basic conception, properties, design approaches and recent study status of SMC, from which we can find some desider-ated problems to be studied. Finally, we introduce the main contents and the background of several important systems and control problems in this thesis.2. In Chapter 2, we introduce the analysis approaches of the stability, controllability and the observability for the switched systems. Firstly, the construction and the existence analysis of CQLF for switched sys-tems are discussed. Moreover, the stability conditions by using CQLF approach are established. Secondly, the stability conditions by using multiply Lyapunov function approach are also established. The switching law design approaches are summarized. The conservatism of the stability conditions obtained by using the above-mentioned two ap-proaches is compared. Finally, the controllability and the observability conditions for the switched systems are given respectively.3. In Chapter 3, we investigate the SMC and the observer designs of a class of switched systems with a nonlinear disturbance based on the multiply Lyapunov function approach. The sliding mode controller and the switching law are designed by using the estimated states, which guarantee the asymptotic stability of the closed-loop systems.4. In Chapter 4, we address the problem of output feedback SMC of switched systems. Firtly, for a class of disturbance-free linear switched systems, we design a sliding function by using only output information, and propose the existence condition of the sliding mode dynamics. Based on the obtained condition, we get the solution to the parameters of the designed sliding function. Also, we synthetize the output feed-back sliding mode controller and the switching law. Secondly, based on the results obtained in this chapter, we further investigate the problem of the reduced-order output feedback SMC of switched systems with nonlinear disturbance. The condition for the existence of sliding mode dynamics is proposed. Also, the controllers for all the subsystems and the switching law are designed, which guatantee the robustness of the closed -loop systems to the unknown disturbance.5. In Chapter 5, our attention is focused on the studying of SMC of dis-crete-time switched systems. Firstly, by applying the feedback control and the rolling optimaization approaches in the predictive control, we design a class of predictive sliding mode controllers, which guarantee the asymptotic stability of the closed-loop system under arbitrary switching. Secondly, as for the robustness-loss of the traditional SMC of discrete-time systems, we proposed a discrete-time SMC strategy containing a recursive sliding surface function. Moreover, the reaching law approaches used in discrete-time SMC systems are improved. In addition, as for the systems with that its uncertainties and disturbances'upper bounds are unknown, an admissible discrete-time SMC law is proposed.6. In Chapter 6, we study the SMC of a class of Markov switching sys-tems. A model transformation is introduced firstly, by which the origi-nal system becomes a"regular"form. A linear sliding surface is de-signed. A sufficient condition of the mean-square exponential stability is proposed for the sliding mode dynamics by using linear matrix ine-quality approach. Finally, a sliding mode controller is synthetized, which guarantees the reachability of the system's trajectories to pre-defined sliding surface in a finite time.The conclusion and perspective are given in the end of the paper.
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