The Guaranteed Cost Control Of Nonlinear Uncertain Time-Delay Singular Systems

It inevitably exists time-delay phenomenon and uncertain phenomenon in most real industrial systems (such as power systems, communication systems, etc). Simultaneously, the nonlinear singular systems are widely appeared in the engineering application, for example:the forecast of hurricane, limited robot, etc. Therefore, it has more theoretical value and practical significance to dedicated to the research of the nonlinear uncertain singular systems with time-delays. Although, the research of the normal system of guaranteed cost control problem is very perfect for contemporary scholars, but as a more general and more complex problems, the study of guaranteed cost control for nonlinear uncertain singular systems with time-delays problem also appear to be defective. At present, the nonlinear guaranteed cost control problem of uncertain singular systems with time-delays has become one of the scholar’s hotspots and difficulty cybernetics research.This paper will aim at studying the guaranteed cost control problem for a class of uncertain time-delay singular systems with nonlinear disturbance, basing on the stabil ity theory and linear matrix inequality (LMI) approach. The specific work arrangement is as follows:The first chapter, it briefly elaborates the general situation of the nonlinear systems, the time-delay singular systems and the guaranteed cost control of the uncertain generalized systems. Secondly, it analyzes the research background, development status and existing problems in detail about the robust analysis and synthesis problem of singular systems.The second chapter, introducing the basic knowledge of mathematics, which this chapter will refer, primarily includes:the Lyapunov stability theory, the construction of Lyapunov function, the concept and solving methods of linear matrix inequality (LMI), the theory of guaranteed cost control for generalized systems with time-delay, the several lemma which are commonly used, etc.The third chapter, aiming at a class of nonlinear singular systems with time-delay parameter uncertainties, the stability of closed-loop system was analyzed and the specific expression for the robust stability was discussed, which basing on Lyapunov method. Then, by means of the LMI technique, we obtained the subsistent condition and design method for the guaranteed cost controller. At last, the final result is given in the form of matrix inequality, and we can solve it by using the LMI toolbox in Mat lab.