On Robust Control Of Uncertain Linear Delay Systems

Linear Matrix Inequality (LMI) has become a very important method to solve many kinds of robust control problems by combining with performance index or constraints of the systems easly. This master thesis focuses on some robust performance analysis and robust controller' design with LMI approaches together with Lyapunov stability theory, and the main works are summarized as the following five aspects:(1) A robust stability criterion for uncertain linear time-varying systems based on LMI is proposed adopting directly the new quadratic term integral inequality without model transformation. Further, a robust state-feedback controller and a dynamic-output-feedback controller are derived by the criterion, respectively, a robust reliable state-feedback controller's design method is provided also.(2) The problem of state-feedback guaranteed cost control for uncertain linear time delay systems 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 observer for the system is considered and an optimal dynamic-output-feedback controller's design method is given.(3) After the research of γ suboptimal H_∞ control for uncertain linear time-varyingdelay, two type of γ suboptimal H_∞ controller's designing methods are proposed with state delay or without state delay information, father, an optimal H_∞ controller's designing method is derived by the minimization of parameter γ.(4) A type of robust D stabilization controller's designing method is proposed after the research of D stability with disk pole control for uncertain linear systems. When system's states can not be observed or be disturbed badly, a robust dynamic-output-feedback D stabilization controller is proposed by dynamoic-output-feedback controller.(5) The combination of new proposed quadratic term integral inequality and LMI technology are extended to nonlinear-interconned Lurie system, a new robustly absolute stability criterion is proposed. Two types of robustly absolute stability criteria with state delay or without state delay information are proposed based on the new obtained stability criterion.Computer simulations have been done for the proposed methods of this thesis, and obtained results show the effectiveness of methods.