Study On Fuzzy Sliding Mode Variable Structure Control Theory For Uncertain Nonlinear Time-delay System

In the 1950s, the concept of Sliding Mode Variable Structure (SMVS) was first raised by Emelyanov-a former Soviet Union scholar. After that, Utkin and Itkis developed its theory. In the 1970s, the SMVS system interested extensive attention of the western countries'scholars because of its unique benefits and characteristics. Many scholars have made in-depth research on the SMVS theory by many point of view. Therefore, this theory has been developing a independent research branch gradually. In recent years, with the development of robust control, adaptive control and fuzzy control theories, the SMVS theory which combined these control theories have aroused interest of many countries'experts and scholars. Particularly, the SMVS theory has become a hot issue.At first, according to the research status and the new practical application requirements of the SMVS theory, this paper researched some questions of the SMVS theory and gave the corresponding results through the inverted pendulum simulation. The simulation result shows the good effect of the SMVS theory.Secondly, the control theory of the uncertain system is an important issue in recent years. At present, there are robust control, adaptive control, SMVC, intelligent control and many other control theories against the uncertain system. The SMVC theory get extensive attention because of its completely robustness to the parameters change and external disturbances which meet the match condition. Based on fuzzy SMVC theory, this paper researched a class of nonlinear uncertain time-delay systems.It is noted that there exist state matrices uncertainties, input matrix uncertainties and external disturbances in the considered systems. The T-S fuzzy model is used to approximate the nonlinear systems. The sliding mode controller is designed to make the fuzzy system global stable by means of Lyapunov theory and linear matrix inequalities. A simulation is provided to illustrate the effectiveness of the proposed method.At last, we make a summary of the whole article and point out the next step of the research.