Tight interval state estimate for discrete‐time descriptor linear systems

• Published in: International journal of robust and nonlinear control Vol. 34; no. 8; pp. 5306 - 5328
• Main Authors: Lamouchi, Rihab, Meslem, Nacim, Raïssi, Tarek
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2024; Wiley
• Subjects: Algorithms; descriptor systems; Discrete time systems; Engineering Sciences; interval analysis; Linear systems; L∞$$ {L}_{\infty } $$ norm; set‐membership state estimators; State estimation; Uncertainty; zonotopic set computation; zonotopic set computation; set-membership state estimators; descriptor systems interval analysis; L ∞ norm
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7265

Summary In this work, two state estimation methods are proposed for a class of discrete‐time descriptor linear systems subject to bounded uncertainties. First, we propose set‐valued estimator algorithm using symmetric boxes to compute rigorous bounds of the system states. The observer gains are calculated using L∞$$ {L}_{\infty } $$ norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed estimator. Second, to obtain tighter state enclosures, zonotopic set computation are developed instead of interval analysis to design a new set‐valued state estimation algorithm. The performances of the proposed state estimation approaches are highlighted on different illustrative examples.