The Absolute Stability And Control Of Lurie Control Systems With Time Delays

Lurie control system is a class of very typical nonlinear system that nonlinear terms are constrained in the finite Hurwitz sector or infinite Hurwitz sector. The research of absolute stability for Lurie control system is very important for the analysis and design of nonlinear control system. In the real Lurie control system, time-delay phenomena usually cause that the response property of the systems become worse, or even cause vibration and unstable phenomena. A lot of uncertain factor in process of establishing models, and various errors and so on, all above phenomena may occur in the real Lurie control systems, at the same time, It would influence the performance index of Lurie control systems. Therefore, it also has an important theoretical and practical significance to study the uncertain Lurie control systems with time-delay.In this paper, the problems of exponential stability and control for Lurie control systems with time-delay have been studied. Based on Lyapunov-Razumikhin stability theory, matrix theory, measure of matrices; delay differential inequality and linear matrix inequality are employed in this thesis. The exponential stability for criteria Lurie control systems, the designing of H_∞controllers for Lurie control systems are studied. The main contents are as follows:1. The exponential stability for two classes of criteria Lurie indirect control systems with time-delay are studied in the thesis. Employed matrix measure and differential inequality method, some criteria of exponential stability for time-delay Lurie indirect control systems are obtained, which generalized and improved some previous results. An example is presented to illustrate the effectiveness of our results.2. The problems of analyzing and designing H_∞state feedback controllers for two class of Lurie control systems with both time-delay and state and control input with norm-bounded by using Laypunov functional method and LMI approach. In addition, a sufficient condition for the given systems with memoryless asymptotal stabilizable and H_∞properties controller is presented in term of a certain linear matrix inequality, and the designing method of theγ-suboptimal state feedback H_∞controllers is obtained by solving the LMI. Finally, an example is presented illustrate the effective-ness and superiority of the design method by using Matlab tool box.3. The analysis of robust stability and design of robust H_∞state feedback for a class of Lurie systems with both time-delay and parameters uncertainties are studied. For the Lurie systems subject to parametric uncertainties and unknown time-delay terms, sufficient conditions for the given systems with robust stability and the designing method of the robust H_∞state feedback controllers are proposed. Furthermore, an LMI based robust H_∞state feedback controller is developed to guarantee both the robust stability and the H_∞performance for the resultant closed-loop systems. Finally, an example is presented to illustrate the effectiveness and superiority of the design method.