Generalized Delay Systems Based On Observer Feedback Control

This paper considers the robust stability and robust stabilization for uncertainsingular linear systems with time-varying delay. Moreover, the method of designingobserver and observer-based control problems are proposed.Firstly, a delay-dependent stability criterion is given to ensure the singular lin-ear systems with time-varying delay is admissible. From the criterion, the robuststabilization problem is solved by state feedback controller which guarantees thatthe resultant closed-loop system is admissible, and a delay-dependent robust sta-bilization criterion and a delay-independent stabilization criterion are respectivelyinvestigated.Secondly, the problem of observer-based non-fragile control is considered for un-certain singular linear systems with time-varying delay. Base on the stability crite-rion obtained previously, observer and observer-based state feedback controllers aredesigned which guarantee the closed-loop system is admissible. Moreover, observer-based non-fragile control problems are considered in order to tolerate some pertur-bations from observer and controller.Thirdly, the problem of functional observer design for a class of linear singularsystems with delayed state and unknown input is considered. Suffcient conditionsfor the existence of this kind of observers are established. And by solving linearmatrix inequality, the functional observer can be obtained.The effectiveness of these designed methods proposed in this thesis are demon-strated by numerical examples and simulation.