The Robust Control For Linear Discrete-time Systems

The model under which the controller was designed was usually different to the real plant, therefore, the modern control theory was hardly used to analyze a practical control system. The differences can be described as the model uncertainties. On the other hand, in a large number of industrial processes, the existence of time delay makes the methodology of system analysis to be more complicates and more difficulties, meanwhile, the existence of time delay is usually a source of instability and deterioration of system performances. So the study of time-delay systems always attracted considerable attention in the control theory literature. In a word, it is of a great importance in theoretical and practical. In recent years, some related research results have been addressed. Therefore, this thesis mainly deals with robust control of a discrete-time state delay systems with uncertainty.Based on Lyapunov stability theory, robust control theory and convex set theory, linear matrix inequality method is adopted in this thesis to study the robust control and non-fragile guaranteed cost control problem of systems described by state space equation with time-varying parameter uncertainties. The aim of this thesis is to investigate the robust stability analysis and synthesis methods for the considered discrete-time state delay systems. The main content of this thesis is as follows:1. For a class of uncertain discrete-time systems with control input constraints and time delay, this thesis addresses the problem of designing an optimal non-fragile guaranteed cost state feedback controller. By the method of linear matrix inequality, the conditions for the existence of non-fragile guaranteed cost controllers are derived. Furthermore, it is shown that these conditions are equivalent to the feasibility problem of a certain linear matrix inequality system, and its solutions provide a parameterized representation of guaranteed cost controllers. Based on that fact, the design problem of the optimal non-fragile guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the convex optimization techniques.2. For a class of discrete-time uncertain systems with time-varying delayed perturbation and time delay, based on Lyapunov stability theory, we study the problem of designing robust controller with delayed perturbation. The sufficient and necessary conditions for the existing robust controller of the system are presented in the form of linear matrix inequality. Furthermore, the largest bound on such perturbation that guarantee discrete-time system stability is formulated by solving a convex optimization problem.