Research On Robust Control For The Uncertain Nonlinear Systems With Input And State Delays

The time delay, nonlinear characteristics and parameter uncertainties are commonexist in practical control system. This made them become three main factors which mustbe considered in control system study. In recent years, the robust control question foruncertain nonlinear systems with time delays has been one of the hot topics in the study ofcontrol theory. For the study of uncertain nonlinear systems with time delays, not onlyshould consider stability, and also should consider some given performance indicators.Based on the analyze, research, absorbing for the existing achievements of domestic andforeign, the article focuses on the robust control problem of uncertain time-delay systemwith state delays, input delays and nonlinear disturbances (contain double delay). Therobust stability problem, the robust and H_∞optimal control problem and the robustH_∞—γstabilization problem were discussed, and got a very good conclusion.For the paper, at first, the basic knowledge about research was briefly introduced.Then, the robust control problem was discussed for a class of nonlinear systems with inputand state delays and nonlinear perturbation (contains double delay). For the system, theproper Lyapunov function was given. And relevant control theory, lemma, and LMImethod was used. A condition which not relies on delay of robust asymptotic stability anda corresponding state feedback controller for the system was derived. But, the results relyon delay have less conservative than it. For this reason, and according to this kind ofuncertain nonlinear system, a kind of new Lyapunov function was structured. A sufficientcondition which relies on delay of robust asymptotic stability for the system was derivedby using relevant knowledge. At the end of research, the feasibility and efficiency of theconditions were verified by numerical simulation.The paper, further, gave a kind of uncertain nonlinear delay system includingnonlinear perturbation (contain double delay) and a kind of performance index of thesystem. For the robust H_∞optimal performance problems and state feedback controllerdesign method of closed-loop system of the nonlinear system with time-delay, they wereresearched by using H_∞control theory, relevant lemma and LMI method. And comparedwith the existing methods by giving numerical examples, the method had smaller conservative of the method was illustrated.The paper finally gave a class of uncertain nonlinear delay systems with input andstate time delay, nonlinear disturbance. For the system, the robust H_∞—γstabilizationwas researched. Based on the robust H_∞—γstabilization theory, the LMI method andrelevant lemma, the criterion of the robust H_∞—γstabilization and robust H_∞γcontroller design method of closed-loop system were given.