Research On Robust Non-fragile H_∞ Control For Uncertain Linear Systems

This paper deals with robust non-fragile H_∞control for two classes of uncertain linear systems with state time-delay. In order to control the systems effectively, the corresponding control laws are constructed based on Lyapunov stability theory and by using linear matrix inequality technique. This paper is organized as follows:In chapter one, the background,the development of the theory and recent research achievements of uncertainty systems are introduced respectively, and also the same issues of time-delay systems, robust control and H_∞control are introduced respectively. Finally, the main tasks of this paper are introduced, and the main results are also presented.The basic knowledge of time-delay systems is introduced. Some definitions and lemmas, which will be used later, are presented in chapter two.In chapter three, the problem of robust non-fragile H_∞control is studied for a class of uncertain time-delay linear systems. The uncertainties exist not only in the controlled system,but also in the gains of the controller. Using Lyapunov theory and Linear matrix inequality method, a sufficient condition of the non-fragile state feedback controllers are derived, The obtained sufficient condition can be rewritten as an linear matrix inequality form in terms of transformed variables. The obtained robust non-fragile H_∞controller guarantees the asymptotic stability of the closed-loop system. Simulation results illustrate that the systems are robust to both the uncertainty of parameters and perturbations of controllers gain.In chapter four, the robust non-fragile H_∞control problem is studied for uncertainty linear systems with multiply time-delay. The robust non-fragile H_∞controller is designed for a class of complex uncertain systems with multiple time-delay. A sufficient condition for the solvability of the robust non-fragile H_∞control problem is proved by choosing a proper Lyapunov function and using linear matrix inequalities. The obtained sufficient condition can be rewritten as an LMI form in terms of transformed variables. The closed-loop system under action of the given controller is asymptotic stable and statisfies H_∞performance. The practical applicability and validity of the proposed method is illustrated by a simulation example.