The Lmi Delay Systems

The research on the time delay systems attracts considerable attention in the control theory literature all along. Linear Matrix Inequality(LMI) has become a very important method to solve many kinds of robust control problems by combining with performance index or constrains of the systems easily.Based on Lyapunov stability theory, also by using linear matrix inequality, we study some kinds of robust control problem for uncertain time delay systems in details. Concerning the time delay systems with uncertainties, the problem of robust criteria and design methods of robust stabilizing controller are investigated by state feedback or output feedback. The results can be classified as delay-independent and delay-dependent. The main contents of this paper are outlined as follows:(1) A robust stability criterion for uncertain linear time-varying systems based on LMI is proposed adopting directly the new quadratic term integral ineqality without model transformation.Further, a robust state-feedback controller and a dynamic-output-feedback controller are derived by the criterion.(2) The problem of state-feedback guaranteed cost control for uncertain linear time delay system is investigated for given quadratic object function, and a design method of guaranteed cost controller with state delay information is derived. When system's state can not be observed or disturbed badly by noise, the problem of guaranteed cost control based on state observe for the system is considered and an optimal dynamic-output-feedback controller's design method is given.(3) After the research ofγsuboptimal H_∞control for uncertain linear time-varying delay, two type ofγsuboptimal H_∞controller's designing methods are proposed with state delay or without state delay information. Further, an optimal H_∞controller's designing method is derived by the minimization of parameterγ.Computer simulations have been done for the proposed methods of this thesis, and obtained results show the effectiveness of methods.