Guaranteed Cost Control For Uncertain Systems With Input Saturation

The saturation characteristics widely exists in almost all kinds of control systems, such as chemical plants, mechanical systems, and communication networks. The input saturation can greatly deteriorate the performance of the systems, and even drive the systems to be unstable. On the other hand, because of the influence of environment, equipments' error under engineering condition, the real system would not precisely equivalent to the mathematical model which we based on for analysis and synthesis. There exist some uncertainties in the mathematical model. Moreover, time-delay is an universal phenomenon existing in control systems which we can not ignore. It is a source of instability and poor performance.In this paper, we firstly analyze the control systems with uncertain parameters and input saturation. It is assumed that the uncertain parameters are of norm bounded. The corresponding robust guaranteed cost controller with memoryless state feedback is given by applying Lyapunov stability theory as well as some inequalities. The controller can make not only the system robust stable but satisfy a given quadratic cost function. Both continuous-time and discrete time systems are studied, the numerical examples are given to shown the feasibility and effectiveness of our method.Then the problem of guaranteed cost control for a class of linear uncertain time-delay systems subject to input saturation is considered. By utilizing Lyapunov-Razumikhin stability theory combining with Leibniz-Newton formula and appropriate matrix inequality technique, both delay-independent and delay-dependent conditions for the existence of the robust guaranteed cost controllers are obtained. The controller parameters can be given by the feasible solution of LMIs. The optimal guaranteed cost controller which minimizes the quadratic cost index is obtained by solving a convex optimization problem with LMI constraints.