The Analysis Of Exponential Stability For Uncertain Neutral Type Descriptor Systems

The neutral type descriptor system is more general and wider than neutral system anddescriptor system, many practical processes can be modelled as general neutral typedescriptor system, such as circuit analysis, computer aided design, real-time simulation ofmechanical systems and optimal control, etc. It contains delays in both its states and thederivatives of states and has the nature of the regular and impulse, so it is used morewidely than neutral system and descriptor system, it can reflect the change law of thingsand reveal the essence of things more profound and accurately. Time delays anduncertainty are important factors which affect the performance of neutral type singularsystem. Therefore, the research for the exponential stability of uncertain neutral typesingular system with time-delays has important theoretical and practical significance.This dissertation studies the problem of delay-dependent exponential stability foruncertain neutral type descriptor system with time-delays by constructing appropriateLyapunov-Krasovskii functional, combining with model transformation, some newintegral inequalities and free-weighting matrix methods. The main works are as follows:Firstly, for the uncertain neutral type systems, by referencing the inequality and linearmatrix inequality methods, the exponential stability problem for a class of neutral typesystems with time-varying delays is discussed.Secondly, thanks to many uncertain factors, the problem for the exponential ofnonlinear neutral system with delay-dependent is considered. A new criterion of theexponential stability for neutral system with nonlinear is given.Thirdly, the problem of the global exponential stability for a class of neutral typesingular system with time-varying is dealt with. Based on Lyapunov-Krasovskii functionalstability theory, using Schur-complement Lemma and a new integral inequality, theexponential stability of neutral type descriptor system is analyzed.Finally, the exponential stability problem of the neutral singular network system isinvestigated. According to Lyapunov-Krasovskii functional method and free-weightingmatrix method, a new delay-dependent criterion for global exponential stability of thesystem is given.