Admissibility Analysis And Robust Filtering Of Linear Generalized Delay Systems

The time-delay phenomenon is considered to be the main cause of the oscillation,instability and poor performance of the dynamic systems,so it has received great attention from scholars at home and abroad.Compared with the regular systems,singular systems can describe the physical systems better,which is widely used in different fields such as economic systems,chemical process,circuit systems,robot systems,network control systems,space navigation systems,biological systems and so on.Therefore,it is of great theoretical and practical significance to analyze and study singular time-delay systems.In this paper,the singular time-invariant delay systems and the singular time-varying delay systems are studied respectively,the main work of this paper is as follows:(1)The problem of robust stability for Singular Systems with time-invariant delay is studied.By constructing an appropriate augmented Lyapunov-krasovskii functional and combining Park intergral inequality,the upper bound of the derivative of the LKF is more tighter.Then,some improved admissibility criteria of corresponding systems are obtained,which reduce the conservatism compared with the previous literature.(2)The problem of robust stability for Singular Systems with time-varying delay is studied.By constructing a novel Lyapunov-krasovskii functional and extend the reciprocally convex approach inspired by Park et al.to analyze the stability of singular systems with interval time-varying delay.Some improved results for the considered systems to be regular,impulse free,and stable are established in terms of LMIs.The obtained stability criteria involve fewer decision variables comparable to those based on the free-weighting matrices method,hence they are mathematically less complex and computationally more efficient.Meanwhile,the new criteria are less conservative than existing ones.(3)The problem of mixed H_? and passive filtering for Singular Systems with time-varying delay is studied.Sufficient strict-LMI-based conditions are derived for the filtering error singular systems to be admissible and satisfy a prescribed mixed H_? and passivity performance index;more flexible conditions are developed for the existence of the mixed H_? and passive filter,in which Finsler lemma and matrix transformation technique are applied,H_? filtering and passive filtering for Singular Systems with time-varying delay can be fulfilled in a unified framework.