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Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems Wang, Ye Olaru, Sorin Valmorbida, Giorgio Puig Cayuela, Vicenç Cembrano Gennari, Gabriela Institut de Robòtica i Informàtica Industrial Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial Universitat Politècnica de Catalunya. SAC - Sistemes Avançats de Control Àrees temàtiques de la UPC::Informàtica::Automàtica i control control theory robust invariant sets active mode detection descriptor systems Classificació INSPEC::Control theory © 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. 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. Postprint (author's final draft) 2017 Conference report Wang, Y., Olaru, S., Valmorbida, G., Puig, V., Cembrano, M. Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems. A: IEEE Conference on Decision and Control. "2017 IEEE 56th Annual Conference on Decision and Control (CDC)". Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 5648-5653. https://hdl.handle.net/2117/119736 10.1109/CDC.2017.8264511 eng https://ieeexplore.ieee.org/document/8264511/ info:eu-repo/grantAgreement/MINECO//DPI2013-48243-C2-1-R/ES/OPERACION EFICIENTE DE INFRAESTRUCTURAS CRITICAS/ http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain 6 p. application/pdf Institute of Electrical and Electronics Engineers (IEEE)