The Stability Of Nonlinear Delay Systems And Lu Of H_ ¡Þ Control

In the paper, stability problems and robust H_∞control for a class of time-delay systems with nonlinear uncertainty are mainly researched. The main contents and contributions in the paper are as follows.Firstly, The stability of the zero solution is discussed for a class of time-delay differential equations with nonlinear. Based on Lyapunov stability theory, the sufficient conditions, asymptotically stable for such equations, are obtained. An example is given to illustrate the theorems.Secondly, The robust stability and H_∞control problem of a class of time-varying delays systems with nonlinear uncertainties is considered. Design the controller on condition that the nonlinear uncertain functions are gain bounded, a sufficient condition, robust asymptotically stable for such systems with time-varying delay and nonlinear, is presented for the existence of the controller based on Lyapunov stability theory and matrix inequality. It is easy to find the solution of the robust optimal state feedback H_∞controller using LMI toolbox. It overcomes the Riccati's shortcomings for solving these problems. An illustrative example demonstrates the effectiveness of proposed method.