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The problem of designing sliding mode controllers investigated the feasibility of the sliding surface combined for a class of linear systems with uncertainties and both input with a predictor to compensate for the input delay of the and time state delays is investigated. A particular linear system. Robust integral sliding mode control for uncertain transformation is defined to transform the time-delay system into stochastic systems with time-varying delay was researched by a delay-free form first. Then, the sliding mode controller is Niu and Ho [9]. designed based on the transformed system. Optimal control The study of uncertain systems with either state-delay or theory is adopted to construct the optimal sliding manifold with a quadratic performance index minimized. The selected control nput-delay has been pad much attention in the past decade law can ensure the existence of the sliding mode and alleviate[7]-[1O]. However, with regard to the control of system chattering effectively in the sliding motion. About the featuring both state and input delays, only a few studies have uncertainties, the cases of matched condition and unmatched been reported in the literature. In this paper, based on SMC, a condition are studied respectively. Furthermore, a sufficient class of linear uncertain systems with both input delay and condition that guarantees the global asymptotic stability of the state delay are investigated. A novel systematic SMC system original system is derived. Finally, a numerical example is given design methodology is proposed. to illustrate the proposed approach.This paper is organized as follows. The next section describes the system that will be studied. In Section III a linear Index Terms -Sliding mode control, uncertain systems, timetransformation is defined to map the original system into a delay systems, optimal control. delay-free form. Section IV presents the design of the sliding I. INTRODUCTION mode controller in detail. The optimal sliding manifold design based on optimal control theory is presented in Section A. Time delay is quite common in various engineering systemsThe design of the control law that consists of a continuous such as chemical processes, hydraulic systems, biological control action and a discontinuous control action is carried out systems and economic systems. Compared to the systems in Section B. A sufficient condition for the asymptotic without delay, the presence of delay makes it more difficult to stability of the original system with the proposed control law achieve the satisfactory performance of the systems. Another is given in Section C. Section V performs a simulation major problem in real-world systems is the robust control to example to verify the effectiveness of the proposed scheme. minimize the effects of uncertainties. In recent years, there is II. PROBLEM STATEMENTS an increasing interest in the development of robust control systems for processes having time delays and uncertainties.Consider the uncertain retarded system described by Many approaches have be...

The problem of designing sliding mode fuzzy controller (SMFC) on the basis of sliding mode control(SMC) theory and fuzzy logic control (FLC) technique is considered. By integrating FLC based on Sugeno inference with sliding mode control, each THEN-part function in the SMFC rule base is a sliding mode control law. Every fuzzy rule in the rule base has its own physical meaning and the generation of the rule base is much easier than that of the conventional fuzzy logic controller. In addition, a moving sliding surface and a boundary layer tuned by fuzzy logic are employed to design the SMFC rule base such that the system properties are improved. Furthermore, the proposed SMFC is applied to an electrical servo drive system. Simulation results verify that the system with SMFC can achieve favorable position tracking performance and robustness when subjected to parameter variations and external load disturbance.Index Terms -Sliding mode control, fuzzy logic control, sliding mode fuzzy control, fuzzy sliding mode control, electrical servo drive.