| In the 1950s, Soviet researcher-Emelyanov first proposed the conception of variable structure. Furthermore, the theory of variable structure system (VSS) was developed by Utkin and Itkis et al.. In the 1 970s, the VSS received extensive attention of the western researchers for its distinct merits and features and it has been deeply studied from the different aspects with many mathematic methods. Now, the VSS already becomes a relative independence research branch. Variable structure control (VSC) is an effective robust control strategy. In the recent years, with the development of all kinds of the control theory, such as robust control, adaptive control, fuzzy control and time-delay system control etc., the theory of VSC has also obtained development rapidly. Moreover, the theory researches and application reports of VSC also appeared in the filed of state estimate, discrete system control, time-delay system control, robust control for uncertain systems, adaptive control, output feedback control and so on.Based on the study status of VSC and the new requirements from the practice for the theory of VSC, some desiderated problems are studied and discussed in this paper, also the corresponding results are given. The main contents are as follows:1.For a class of nonminimurn-phase uncertain linear systems, the design approach of a new fuzzy integral sliding mode control (SMC) is presented. The integral operator is introduced such that the control system achieves a zero steady state error. The frizzy logic control is used to estimate the unknown uncertainties, and guarantees the robustness of the closed-loop system in the reaching phase synchronously. By the reaching condition, the stability of fuzzy controllers is assured.IvSimulation results show that the closed-loop system has the better robustness and zero steady state error. In addition, when the matching conditions are satisfied, the proposed method can also be used for nonminirnum-phase system.2.For a class of uncertain time-varying time-delay linear systems, which don't satisfy the matching conditions, a new adaptive VSC strategy is proposed based on Lyapunov stability theorem. The control strategy can guarantee the existence of sliding phase for the closed-loop system. Since the conventional matching conditions are no longer matched, the coefficient matrix of sliding function can be designed to satisfy a new matching condition. It is shown that the system is invariant on sliding surface. Once the dynamics of the closed-loop system come into the sliding mode, the motion should continue on the sliding surface, and the global stability of the closed-loop system is guaranteed. Furthermore, we also study a class of large-scale systems with uncertain interconnected time-delay, which don't satisfy the matching conditions, and a new decentralized VSC strategy is proposed.3.Based on the discuss and summarize for the merits and shortcomings of current terminal sliding mode, a new terminal SMC technique is given for a class of high-order nonlinear dynamic systems. A mathematical expression is proposed to choose the terminal sliding surface for n -order systems. In addition, all the system states are on the sliding hyperplane at the initial instant, the reaching phase of SMC is eliminated and the global robustness and stability of the closed-loop system can be guaranteed with the proposed control strategy. Considering that the unknown upper bound of uncertainties, which include parameter variations and external disturbances, we also propose a terminal SMC technique with a simple adaptation laws to overcome the above limitation4.For a class of nonlinear dynamic systems with input nonlinearity, a new sliding mode controller is proposed to deal with the tracking problem.VAnd combining with the study of the terminal sliding mode, the design methods of an adaptive terminal SMC is developed for a class of high-order nonlinear dynamic systems with input nonlinearity. Then we also study the parameter identifica...
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