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Using set invariance to design robust interval observers for discrete‐time linear systems
Author(s) -
Meslem N.,
Loukkas N.,
Martinez J.J.
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4103
Subject(s) - control theory (sociology) , observer (physics) , interval arithmetic , discrete time and continuous time , bounded function , mathematics , interval (graph theory) , computation , state vector , interval estimation , state observer , linear system , robustness (evolution) , computer science , nonlinear system , algorithm , statistics , artificial intelligence , control (management) , confidence interval , combinatorics , mathematical analysis , biochemistry , physics , chemistry , quantum mechanics , classical mechanics , gene
Summary Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H ∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.