Robustness of linear time-varying systems with relaxed excitation

Denis Efimov 1 Nikita Barabanov 2 Romeo Ortega 3
1 VALSE - Finite-time control and estimation for distrubed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : It is a well-known fact that linear time-varying systems with a persistently excited state matrix are exponentially converging and input-to-state stable with respect to additive perturbations. Recently, several relaxed conditions of persistent excitation have been presented [1], [2], which ensure an asymptotic convergence rate in the system. In the present work it is shown that these conditions are similar, and that under such a relaxed excitation only non-uniform in time input-to-state stability and integral input-to-state stability properties can be obtained. The results are illustrated by simulations for a problem of estimation in the linear regression model.
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Denis Efimov, Nikita Barabanov, Romeo Ortega. Robustness of linear time-varying systems with relaxed excitation. International Journal of Adaptive Control and Signal Processing, Wiley, 2019, ⟨10.1002/acs.2997⟩. ⟨hal-02082769⟩

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