Stability Analysis For Three Types Of Uncertain Discrete Time-Delay Systems

In many kinds of systems, the time-delay systems exist widely, the existence of the time-delay makes the stability analysis much more complicated, and the existence of the time-delay make the stability much more uncertainly. The study of the uncertain time-delay systems became a hotspot and had attracted more and more researchers. It has profound theory significance and practical value to investigate the stability analysis and synthesis problem of the uncertain time-delay system.Based on Lyapunov stability theory and linear matrix equality (LMI) technology, this paper studied the stability problems and robust control problems of the uncertain time-delay systems. Sufficient conditions are given in terms of LMI to ensure the stability of the uncertain time-delay systems. Compared with some existing results, the criteria obtained in our paper are less conservative. The main works as following:In the first chapter, the problem of this background of this paper and the state of study in the uncertain time-delay systems were presented. In the second chapter, the corresponding preliminary information was given. In the third chapter, the asymptotic stability of the neutral systems with norm-bounded uncertainties and time-varying delays were discussed by using the method of LMI. the sufficient condition of robust stabilization of the neutral systems with norm-bounded uncertainties and time-varying delays with nonlinear perturbation is given. The results were expressed in terms of linear matrix inequalities. Compared with some existing results, the criteria obtained in our paper are less conservative. In the forth chapter, the stability analysis of generalized delayed neutral network with mixed discrete and distributed delays were devoted. The stability analysis problem is converted into a convex optimization problem, and a linear matrix inequality (LMI) approach is utilized to establish the sufficient condition for the globally robust stability. This condition can be easily checked by using the MATLAB LMI Toolbox. In the fifth chapter, for linear time-delay systems with norm-bounded uncertainties, a sufficient and necessary delay-dependent condition of asymptotic stability and the corresponding robust stabilizing controller designing methods were given in the terms of linear matrix inequalities. The results can be solved easily by using LMI toolbox in MATLAB. In the last, we sum up this paper and give some expectations of the neutral time-delay systems study.