Delay-Dependent Robust Control Algorithm For Uncertain Discrete Time-Delay Systems

In engineering applications, it is usually impossible to describe a practical system exactly. First, parameters or parasitic processes are not completely known. Second, due to the limitation of mathematical tools available, a relatively simple model is often used to approximate a practical system so that the controller design is possible. However, some aspects of the system dynamics are ignored. Third, some control systems are required to operate within a wide range of different operating conditions. Robust control theory is often possible to identify a bounding set such that all the admissible uncertainties fall within this set and yet it is not too difficult to analyze mathematically. On the other hand, owing to ubiquitous presence of transmission process and complicated on-line analyzer etc. in industrial processes, time-delay systems have been an active area in scientific research.Based on the Lyapunov stability theory and convex set theory, the problem of delay-dependent robust stabilization for uncertain time-delay systems is addressed in this dissertation. By using linear matrix inequalities (LMIs), robust stability criteria are obtained, which are also extended to the design algrithm of robust stabilizing controller and guaranteed-cost controller that not only robustly stabilizes the uncertain systems but also guarantees certain cost. The main contents of this dissertation are outlined as follows:1. The problem of robust stabilization for discrete time-delay systems with norm-bounded uncertainties is studied. By introducing a zero-formula with slack variables so as to express the relationship between the terms in the zero-formula, a sufficient condition of delay-dependent robust stabili-zability is devised based on LMIs. An explicit expression of the desired state feedback controller is also developed.2. The problem of robust stabilization for discrete time-delay systems with polytopic uncertainties is studied. Based on descriptor system transformation, a parameter-dependent Lyapunov functional is constructed to derive robust stability condition and the state-feedback control law via LMIs. Numerical example shows its effectiveness.3. The problem of guaranteed-cost control for discrete time-delaye systems with norm-bounded uncertainties is considered. Attention is focused on the design of state feedback controller such that the resulting closed-loopsystem is asymptotically stable and an adequate level of performance is also guaranteed. By using a descriptor model transformation and a zero-formula with slack variables, a delay-dependent sufficient condition for the existence of guaranteed-cost controller are also presented in terms ofLMIs. The conclusion and perspectives are given in the end of the dissertation.