Exponentially Stable Stubborn Observers for Discrete-Time Linear Systems (Extended Version)
Résumé
State estimation is crucial for control and monitoring of dynamical systems, but sporadic disturbances (outliers) can severely degrade the estimator's performance. This paper studies the stability of a so-called "stubborn" observer, designed to mitigate the effects of outliers, for discrete-time linear systems. We prove that the detectability of the system is both necessary and sufficient for global exponential stability of the observer, providing an improvement over existing results that rely on potentially infeasible LMI conditions. The proof is constructive, leading to practical guidelines for selecting the observer parameters. Numerical simulations demonstrate the observer's effectiveness in mitigating outliers and its superior performance compared to a classical Luenberger observer.
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