Robust filtering for uncertain linear discrete-time descriptor systems (original) (raw)
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The robust filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the "fast" subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.
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LESSI, Département de Physique Faculté des Sciences Dhar El Mehraz B.P : 1796, 30000 Fes-Atlas Morocco. E-mail: hmamed_a@fsdmfes.ac.ma E-mail: elhafidchelliq@caramail.com . Abstract AA New robust sufficient stability condition for uncertain continuous-time systems with convex polytopic uncertainty are given. They enable to check stability using parameterdependent Lyapunov functions which are derived from LMI conditions. A descriptor system approach is taken to deriving linear matrix inequality LMIs conditions. The proposed conditions are less restrictive than other parameter dependent based methods from the literature providing better results as illustrated by means of numerical examples. The reduction of the conservatism is illustrated by a numerical evaluation.
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In this paper, the computation of robust invariant sets for discrete-time uncertain descriptor systems is investigated. The studied descriptor systems are assumed to be regular and stable subject to unknown but bounded disturbances. The robust invariant sets of both causal and non-causal descriptor systems are studied. Transformations for causal and non-causal descriptor systems are used in the characterization of the effect of the disturbances. For causal descriptor systems, two robust positively invariant (RPI) sets are computed separately. For non-causal descriptor systems, an RPI set and a robust negatively invariant (RNI) set can be found. As a result, the general RPI set of a descriptor system can be obtained from a linear projection image of these two sets. Besides, active mode detection method is proposed based on set invariance theory.