Stability Analysis Of Generalized Delay Systems

Singular systems can provide a more natural presentation of dynamic behaviour than the standard systems due to the fact that singular systems can reflect non-dynamic algebraic constraints of state variables more accurately. Time delay appears in many dynamic systems which may cause poor performance and even instability. The last decade has seen an increasing attention on singular time-delay systems. Singular systems have much more complicated forms than those of standard systems and need to consider not only stability, but also regularity and non-impulsiveness. Therefore, the subject of singular systems is of both theory and practical value, and has been one of the fundamental problem in the control theory.This thesis is concerned with the analysis of stability for singular time-delay systems.By using augmented Lyapunov-Krasovskii functionals, reciprocally convex combination and Wirtinger based integral inequality methods, we obtain new stability criteria in terms of a strict linear matrix inequality. Illustrative examples show the effectiveness and merits of the methods.For singular systems with constant time delay, by representing the singular system as a neutral form, using an augmented Lyapunov-Krasovskii functional and the Wirtinger-based integral inequality method, we obtain a new stability criterion in terms of a linear matrix inequality. Some examples are provided to illustrate the effectiveness and the benefits of the proposed method.For singular systems with interval time-varying delays, a delay-derivative-dependent stability criterion is given in terms of linear matrix inequalities which can produce allowable delay bounds as large as possible and the number of decision variables as few as possible. The main techniques used are the Wirtinger based integral inequality and augmented Lyapunov functional method that employs much delay information. Several classical examples show the effectiveness and merits of the method.