Research On Robust Stability And Robust Control For Uncertain Time-delay Systems

Time delay, widely existing in the practical systems, often is one of the main reason of causing the system performance deterioration and even instable. Delay-dependant results have less conservative than the delay-independent ones, for the results of delay-dependent stability and control provide the size of delays such that the systems keeps stable. Therefore, many researchers pay much attention and make some efforts on it. So the study of delay-dependent stability and control for the time-invariant delay systems and time-varying delay systems is significant.The research mainly comes from the supports of National Nature Science Foundation of China (Key Project No. 60334010, Project No. 60474047); SRFDP (Project No. 20030561013), and Guangdong Province Natural Science Foundation of China (Project No. 31406). In terms of Lyapunov-Krasovskii functional, matrix inequality tactics, and the method for dealing with nonlinear term, delay-dependent stability and control of the time invariant delay systems and time-varying delay systems, even with nonlinear perturbations, are systematically studied, such as H∞ robust stability, output feedback H∞ robust control, Hoo robust control for discrete time delay systems, absolute stability for Lurie uncertain time-delay systems and robust stabilization of networked control systems. Main studies include as follows:1. A new stability criterion of linear uncertain systems with multiple delays is obtained based on the related theory of spectral radius and modulus matrix by the frequency domain method. The results are presented based on the assumption that system matrix A is a Hurwitz one and there is no requirement of a negative matrix measure.2. Delay-dependent stability of uncertain time-varying or time-invariant delay systems with nonlinear perturbation is studied. Based on Lyapunov-Krasovskii functional and matrix inequality methods, sufficient conditions of delay-dependent H∞ robust stability are presented.3. Absolute stability of uncertain multiple time-varying or time-invariant delay Lurie direct control systems and uncertain multiple time-varying delay Lurie indirect control systems are studied. In terms of matrix inequality technique and the method for dealing with nonlinear term, new sufficient conditions of delay-dependent absolute stability are provided, which by some examples are...