Observer-Based Stabilization Control of Time-Delay T-S Fuzzy Systems via the Non-Uniform Delay Partitioning Approach

Abstract

It is well known that intelligent control technology plays an important role in the design of many control systems, and intelligent control has aroused wide attention from scholars. Fuzzy control is also the case because fuzzy control is one branch of intelligent control. The Takagi-Sugeno (T-S) fuzzy model is an effective approach when dealing with complex nonlinear systems, and the advantages of fuzzy controller design is that the linear control methods can be used. In addition, nonlinearity and time delay are inherent and not all states are available in many practical system. Therefore, the observer-based stabilization control for time-delay T-S fuzzy systems is of great significance. With the help of the non-uniform delay partitioning approach, a novel method is put forward to analyze the stability of the time-delay T-S fuzzy system and design the observer-based feedback controller via the parallel distributed compensation (PDC) scheme. The sufficient conditions of asymptotic stability for both nominal and uncertain time-delay T-S fuzzy system are derived based on the Lyapunov stability theory and linear matrix inequality (LMI) techniques. What is more, the solving methods to obtain the controller gain matrices, observer gain matrices, and upper bound of time delay are presented. Two illustrative examples are given to demonstrate the effectiveness and verify the superiority of our developed methods. From the simulation results, it can be found that the most prominent advantages of our proposed methods lie on larger delay bound and less decision variables compared with other related methods. The problem of observer-based stabilization control for continuous nonlinear time-delay systems is investigated in this paper, and the delay-dependent stability criteria are derived to achieve greater delay bound by virtual of the non-uniform delay partitioning approach. Numerical examples further confirmed the effectiveness and advantages of our developed methods.