Meslem, N.; Loukkas, N.; Martinez, J. J. Using set invariance to design robust interval observers for discrete-time linear systems. (English) Zbl 1398.93052 Int. J. Robust Nonlinear Control 28, No. 11, 3623-3639 (2018). 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 offline 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 online 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 \(H_\infty\) method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples. Cited in 6 Documents MSC: 93B07 Observability 93B35 Sensitivity (robustness) 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93B50 Synthesis problems 93B36 \(H^\infty\)-control 65G30 Interval and finite arithmetic Keywords:bounded error; \(H_\infty\) synthesis; interval analysis; minimal robustly invariant sets; set-membership state estimation PDFBibTeX XMLCite \textit{N. Meslem} et al., Int. J. Robust Nonlinear Control 28, No. 11, 3623--3639 (2018; Zbl 1398.93052) Full Text: DOI