Analysis On Robust Control For Nonlinear Time-delay Systems Based On T-S Model

As the focus of control theory, the stability analysis and synthesis of nonlinear time-delay system have long been attached much importance. In recent years, T-S fuzzy model method for its own local linear approximation characteristics that have become an important method to study nonlinear time-delay system.Through the establishment of the T-S fuzzy model of the system, combined with the L function method and linear matrix inequalities technology, this article study the stability, robust fuzzy control and H∞performance of nonlinear time-delay systems, the main content and the results are embodied in the following aspects:1) From the perspective of practical application, this article sets time-varying delay the lower bound are not strictly zero, and study a class of interval time-varying delay system with nonlinear perturbation. By constructing a new kind of L-K functional with adjustable parameter, a new delay-dependent stability criteria with adjustable parameters are proposed via LMI approach. Some numerical examples have shown that the obtained results are less conservative.2) A combination of descriptor model transformation approach and Moon s inequality technique which is effective method to deal with the linear time-varying delay systems are extended to the T-S fuzzy time-varying delay systems,and study for a kind of uncertain continuous composite robust control of time-delay systems. Based on improved L-K functional with adjustable parameters, in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened and the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.3) Based on the results of uncertain systems with composite time-delay, H∞robust control problem is solved for the system with a disturbance outside,via LMI approach, a new containing adjustable parameters of delay-dependent robust stabilization of H∞sufficient conditions is given, and H∞robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened, the system H∞performance index can be reduced and the indirect regulation on the controller can be realized by changing adjustable parameters.The simulation example verify the effectiveness of the conclusion obtained.4) The technology used in the continuous delay-system stability control reasonably is applied to the research about robust control of a class of uncertain discrete system with composite time-delay. Using the forward difference function y(k) of the system to do the transformation, and with the help of integral and summation relationship,constructing a kind of new discrete L functional with adjustable parameters, that fully contains delay informations,in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed.On the basis of the closed-loop systems stable, the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.