An LMI Approach To The Stability Analysis And Stabilization For Delay Systems

It is well known that the phenomenon with time-delay can be found in the most of industrial processes owing to the actions from transmission, measure and so on, and often results in the instability and poor performance. Stability and performance are always the key issue in the control theory and control engineering, so the study of delay systems attracts considerable attention in the control theory literature. Meanwhile, As well known, it is almost impossible to obtain accurate mathematics models for the object systems due to the complex dynamical behaviors in the practical control process. The model under which the controller designed is usually different to the real plant owing to some kinds of model approximation or reduction methods, and the difference can be regarded as a certain uncertainty. Therefore, more values can be obtained from the research into the delay systems with uncertainties.By using the Lyapunov second method, linear matrix inequalities and matrices analysis, this paper studies stability, memory state feedback control, and guaranteed cost control. The main works is illustrated as following:At first, the background of the research into stability and stabilization of time delay systems is introduced. In the first chapter, some basic notions are introduced, which are mainly categorized into four parts:(l) Conception of LMI; (2) LMI Toolbox; (3) Conception of S-procedure; (4) Relative lemmas; (5) Explanation of Nomenclature. In the second chapter, uncertain time delay systems and time delay systems with nonlinear perturbations are studied. A new approach is introduced to analyze the linear uncertainties of delay systems. This approach yields a less conservative stability condition for a class of uncertain time delay systems. An illustrative example is given to indicate that the criterion in this paper is less conservative than the former results. In the third chapter, the stability problems of uncertain neutral delay systems and neutral delay systems with nonlinear perturbations are researched. In the fourth chapter, the stabilization problems of uncertain neutral delay systems are researched. At first, the memory state feedback controller is designed. Based on it, Guaranteed cost controller is studied. The results are shown by linear matrix inequalities. At last, we sum up all the paper and prospects of the time-delay systems studies.