Research On Robust H-infinity Control Methods Of Nonlinear System Based On The T-S Model

Nowadays, more and more engineering system have the phenomenons such as highly nonlinear, uncertainty and time-delay, mathematical model become incapable to accurately describe system. T-S fuzzy model of nonlinear system has good approximation ability, and widely used for analysis, using the T-S fuzzy model of fuzzy control is a successful method to solve the problem of nonlinear control system based on the research T-S fuzzy model of nonlinear systems with delay the stability analysis and controller design problem. Robust h-infinity control is a successful method of solving uncertain and time-delay problems, this article will both combine, find a meet h-infinity norm bounded under the restriction of quadratic stability controller design method.Based on the T-S fuzzy ideas, T-S fuzzy model was used to approximate a nonlinear systems, then, based on piecewise linear system, we analysis the stability of system and design the controller. The article content is divided into two parts:the first part contains T-S fuzzy systems for stability analysis and contains no time-delay nonlinear system robust h-infinity controller design, use PDC (Parallel Distribution Compensation) method, distributed that compensation system stability, conditions, for example through the simulation results of the algorithm and the article concludes that the effectiveness of the result;The second part contains T-S fuzzy time-delay systems stability analysis and for a class of uncertain time-delay nonlinear system with the robust h-infinity controller design, using a piecewiss smooth Lyapunov function, gives the system stability conditions, through the simulation results of the algorithm and the article concludes that the effectiveness of the result.Based on current research method of the stability of time-delay, this paper mainly points out some limitations, introducing a new Lyapunov-Krasovskii functional theory, and puts forward a delay-dependent stability of research method, the new method of integral inequality (II), discussed the system, because the new conditions with Lyapunov-Krasovskii functional theory is more strict, the conclusions obtained are more conservative than other literature theory.Secondly, the fuzzy modelings of nonlinear systems, using PDC structure design, avoid the controller for public matrix of the difficulties, subsystem design controller makes its stability, and the whole system controller for each local controller, thus to differentiate the weighted and overall system is asymptotically stable condition. Finally based on fuzzy modeling inverted pendulum, a nonlinear model of the inverted pendulum accurate linearization, establish T-S fuzzy model of its application to solve nonlinear robust control problems, through the simulation results verify the result of this chapter. Lastly, aiming at a class of uncertainty nonlinear system model, based the T-S model, a method of quadratic stability state feedback control is gived. Take a piecewiss smooth Lyapunov functions of linear matrix inequality (LMI) method, and gives a fuzzy system of quadratic stability state feedback controller is sufficient conditions of the existence of. Ensure the fuzzy asymptotic stability of the closed-loop system, through the simulation results verify the result of this chapter.