Delay-dependent Robust Control For Uncertain Neutral Type Descriptor Systems

The neutral systems with time-delay is a class of time-delay systems broader thanothers, which can reflect deeper and more exactly the rule of the change of things andreveal the nature of things. Many time-delay systems can be transformed into neutralsystems to study, and it can be found in such systems as population ecology, electriccurrent in transmission problem, heat exchangers, the circuit network system, etc. Timedelays and uncertainty are important factors which affect the performance of neutralsystems. Therefore, the research for uncertain neutral systems with time-delays hasimportant theoretical and practical significance.This dissertation studies the problem of delay-dependent stability and robust controlfor uncertain neutral type descriptor system with time-delays by constructing appropriateLyapunov-Krasovskii functional, combining with model transformation, integral inequal-ity and free-weighting matrix method.The main works are as follows: The delay-dependent problem of stability of neutraltype descriptor systems with multiple delays is considered；For both cases of additive andmultiplicative controller uncertainties, a delay-dependent non-fragile robust H_∞controlproblem of neutral type descriptor systems is investigated. A sufficient condition of theclosed-loop system is given to show the internally stable, and the design method ofnon-fragile controller is obtained too；The problem of observer-based robust passivecontrol for uncertain neutral type descriptor Markov jump systems with time-varyingdelays is dealt with. Based on Lyapunov-Krasovskii functional stability theory, usingSchur-complement Lemma and integral inequality, a delay-dependent robustly passivecondition for closed-loop system is obtained；The problem of dynamic H_∞outputfeedback control for uncertain neutral type descriptor Markov jump systems withtime-varying delays is considered. Based on Lyapunov-Krasovskii stability theory, adelay-dependent sufficient condition, which can ensure a given robust H_∞performancevia an output-feedback controller, is obtained. Then, the design method of controller ispresented in the form of LMI；The problem of robust absolute stability of uncertain neutral Lurie systems with time-delay is investigated. According to Lyapunov-Krasovskiifunctional methord and free-weighting matrix method, a delay-dependent criterion forabsolute stability of the system is given in finite sector.