The Research On Robust H_∞control For A Class Of Nonlinear Systems With Time-Delays

Recently, with the development of the control theory and the practical applications, the robust control of nonlinear system is becoming the frontier of the research of the control theory. Although a large number of theories and methods have emerged with a lot of problems solved, the discussion of the robust control of nonlinear system with time-delay is far beyond satisfactory. In this paper, the robust control problem of several classes of nonlinear systems with time-delay with various uncertainties is discussed, hoping to make some modest contribution to the solving of the problem.Firstly I discuss the Hx control of a class of systems satisfying Lipschitz condition with time-delay dependence using Lyapunov-Krasovskii functional to give a feed-back control of the system. The simulation shows its feasibility.Then the delay-dependent robust control of an interval time-varying time-delayed nonlinear system is discussed. An estimate which is more efficient than the upper bound of the derivative of the Lyapunov function is obtained by dividing the delay and the use of Jensen’s inequality. Then the estimate is expressed as a convex combination. The sufficient condition of delay-dependent stability of the nonlinear system is obtained, and can be expressed as a linear matrix inequality.At last, I discuss the robust stability and robust control of a class of time-delayed systems of which with norm-bounded uncertainty, using Lyapunov stability theory, combining with the linear matrix inequality and the free weighting matrices, getting the sufficient condition of the state feedback robust quadratic stability of the system, establishing convex optimization problem with some linear matrix inequality constraints, obtaining the optimal uncertain system’s state feedback control law.