Robust Control Of Singular Systems

Singular time-delay systems are also named delay differential - algebraic equations, implicit time-delay systems or generalized system delay, It is essentially a system coupled by time-delay differential equations and matrix difference equations. There is no stability conclusion in singular time-delay systems as completed as traditional Lyapunov stability theory in normal time-delay systems. Thus we need to expend Lyapunov stability theory. The systems which have some variables with a small parameter (non-negative) on the time derivative in system state model are named singularly perturbed systems. Singular perturbation theory is an effective tool for analyzing and modeling systems with ill-defined numerical characteristics.In this paper, we research guaranteed cost control of uncertain singular time-delay systems and robust state feedback of uncertain singularly perturbed systems. Main results of this paper include the following two parts:1. Guaranteed cost control of uncertain singular time-delay systems The problem of the robust guaranteed cost control for the continuous linear systems with uncertain parameters and nonlinear perturbation is studied. It is assumed that uncertain parameters are of norm bounded uncertainty, and nonlinear perturbation is general nonlinear function of the state. We can expend Lyapunov stability theory to uncertain singular systems. With inequality handling technique, the guaranteed cost control (GCC) problem can be transferred into solving of linear matrix inequalities. The designs of the robust guaranteed cost controller with memory or memoryless robust guaranteed cost controller are obtained, and then the corresponding examples are given to illustrate the case.2. State feedback control of singularly perturbed systems We research both the state feedback controllers of singularly perturbed systems and the singularly perturbed time-delay systems. Based on the traditional Lyapunov method, the corresponding sufficient conditions for the existence of state feedback controllers are obtained. Some controllers of singularly perturbed systems are obtained by constructing appropriate Lyapunov functionals and by applying relevant inequalities. The controller parameters can be given by the feasible solution of LMIs.The conclusions in this paper is mainly expressed as LMIs, therefore Matlab can be used to obtain the solutions, conveniently. Then we give relative numerical examples to demonstrate the feasibility and effectiveness of the results obtained.