State Feedback Controller Design For Linear Uncertainty 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 and synthesize a practical control system. The differences can be described as the model uncertainties. On the other hand, the existence of delay was frequently a source of instability and deterioration of system performances, so the study of delay systems always attracted considerable attention in the control theory literature. Otherwise, the existing robust control design method just considered the uncertainties of the system parameters, it did not consider the uncertainties of the controller gain. However, the uncertainties often appeared. So people were also interested in the non-fragile control problem.Based on Lyapunov stability theory, through using linear matrix inequality and matrix analysis as the main mathematical tools, this dissertation studied the robust control problem of systems described by state space equation with norm-bounded time-varying parameter uncertainties. The robustness analysis and synthesis methods for the considered uncertain systems were developed in this dissertation.The major contributions of this dissertation were as follows:The problem of non-fragile H₂control for linear systems was concerned in the presence of controller gain variation. The controller to be designed was assumed to have norm-bounded additive controller gain variations. The sufficient condition for the existence of non-fragile H₂control problem for linear uncertain systems was also studied by the same method. And a sufficient and necessary condition was proposed to solve the above problem. A numerical example was given to illustrate the design procedure and its effectiveness.Deals with the problem of robust and non-fragile H_∞control via state feedback for linear systems with norm-bounded parameter uncertainties based on a method of linear matrix inequality. The sufficient and necessary condition for the existence of solutions to the problem was presented in terms of one LMI. The problem of non-fragile H₂ /H∞control for linear systems was concerned in the presence of controller gain variations. The sufficient and necessary condition for the existence of non-fragile controller was presented via linear matrix inequality (LMI). A numerical example illustrated the effectiveness of the design procedures.The problem of guaranteed cost control for a class of uncertain time-delayed systems was addressed. The uncertainties existed both in the systematic matrix, and in the controller gain. And the design methods for resilient guaranteed cost control under two classes of perturbations, additive and multiplicative, were given respectively.