Guaranteed cost control of the actuator saturation systems with uncertain parameters and nonlinear perturbation

For actuator saturation systems subject to parametric uncertainties and nonlinear perturbation, the nonlinear terms of the system model are dealt with by using the linear differential inclusions method. The guaranteed cost control problem is solved via the convex hull method. It is assumed that the uncertain parameters are of norm bounded uncertainty, the nonlinear perturbation is the general nonlinear function of the state, which satisfies norm bound. For this parameter uncertainty situation, using Lyapunov stability theory and linear matrix inequality method, to give the state feedback robust guaranteed cost control law of the corresponding system, and design the guaranteed cost controller. Furthermore, the controller synthesis problems are transformed into the LMI constrained convex optimization problems. That the optimal guaranteed cost controller can make the system robust stability and the quadratic cost function satisfies a certain cost index. Then the corresponding examples are given to illustrate the case.