Stability Analysis Of Neutral Systems

Delay phenomenon are frequently encountered in many fields of science and engi-neering. The existence of time-delays may lead to oscillation, divergence or instability.Moreover, time-delays of neutral systems exist not only in its states, but also in thederivatives of the states, that makes the system much harder to stabilize. Therefore,the subject of the stability analysis of neutral systems is of both theory and practicalvalue, and has attracted considerable attention during the past two decades. Based onLyapunov stability theory, the stability of neutral systems with constant delays, neutralsystems with time-varying delays and neutral systems with distributed delays is ana-lyzed. The main results are as follows:1. During the study of the stability of retarded delay system, discrete delay intervaldividing approach is adopted and improved in this dissertation. By employing newform of Lyapunov functions, less conservative criteria are obtained. Then the approachis applied to two classes of the neutral systems with constant delays(identical discreteand neutral delay, different discrete and neutral delay). It proves that the approach isapplicable for both discrete delay and neutral delay.2. For stability of systems with time-varying delays, other than the restriction ofcurrent method, time-varying delays are discussed in different intervals, more negativedefiniteintegraltermsareutilizedandlesstimesofamplificationaremade. Onthebasisof improvement of current method, combining with delay dividing approach, more con-servative results are derived. For the neutral systems with time-varying delay, makingthe best of information of time-varying delays, and employing the new method of deal-ing with the time-varying delays, the results are applicable for not only quick varyingdelay but also slow varying delay. Then numerical examples are given to demonstratethe effectiveness of the results.3. By delay interval dividing approach, the robust stability of neutral systemswith distributed delays and time-varying structured uncertainties is studied, the discretedelay-dependent, neutral delay-dependent and distributed delay-dependent criteria areobtained.4. Base on the double-staged dissolution tank in chemical process, a class of bi-linear neutral systems are modeled, according to the idea of delay interval dividing,asymmetrical delay interval dividing approach is employed, the stability of the systemsis analyzed and design of controller is researched. In the end, the summarization and the perspective of future research of neutralsystems with constant delays and neutral systems with time-varying delays are given.