The Study On Robust Control For Uncertain Singularly Perturbed Systems

It is usually impossible to describe a practical system exactly in most engineering applications. The changing of running environment and aging of element would cause uncertainties in a control system. Robust control which aim is to design a control law to stabilize the resultant closed-loop system that would satisfy some prescribed performance for all admissible uncertainties is an advanced control theory. On the other hand, a reduced-order model is often used to approximate a practical system due to the complexity of objective controlled, when there is small parameter perturbation especially. Singular perturbation technique is such an effective approach for multiple-time-scale systems such as auto, aerocraft, power system, nuclear reactor, chemical process, circuit, robot and space that it has attracted much attention.The robust stabilization problem for uncertain linear singularly perturbed systems is studied in this thesis. For discrete-time systems, the robust stability and stabilizability for singularly perburbed system with uncertainties is investigated firstly. Secondly, for continuous-time systems, the problems of robust stabilization for time-dalay system and robust H_∞control are studied on the basis of Lyapunov theory and linear matrix inequality(LMI). The main contents of this thesis are outlined as follows,1. The problem of robust stability for a class of discrete-time linear singularly perturbed systems with nonlinear uncertainties is studied. A sufficient condition and the bound of singularly perburbed parameter e* are presented by using Lyapunov theory and decomposing original system to fast and slow subsystems;2. The problem of robust stability and stabilizability for two classes of discrete-time linear singularly perturbed systems with norm bounded uncertainties is investigated. Based on an equivalent Lyapunov inequality, sufficient conditions for the existence of stabilizing control law are given in terms of LMIs. When LMIs are feasible, the explicit expression of state-feedback control andε~* are given at the same time;3. The problem of delay-dependent robust stabilization for uncertain continuous-time linear singularly perturbed time-delay system is addressed. A fitted Lypunov function is constructed to derive a delay-dependent andε~*-dependent condition of robust stability and the explicit expression for the corresponding state-feedback control law is given;4. A LMI approach to the robust H_∞control of uncertain continuous-time linear singularly perturbed system is developed. By descriptor system transformation approach, a new bounded real lemma for linear singularly perturbed system is proposed, which isε~*-dependent. The desired state-feedback control law is also obtained.