Using set invariance to design robust interval observers for discrete‐time linear systems |
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| Authors: | N. Meslem N. Loukkas J.J. Martinez |
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| Affiliation: | Université Grenoble Alpes, Grenoble Images Parole Signal Automatique‐lab, UMR 5216 CNRS, Grenoble, France |
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| Abstract: | 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. |
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| Keywords: | bounded error H∞ synthesis interval analysis minimal robustly invariant sets set‐membership state estimation |
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