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Robustness of linear time‐varying systems with relaxed excitation
Author(s) -
Efimov Denis,
Barabanov Nikita,
Ortega Romeo
Publication year - 2019
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2997
Subject(s) - control theory (sociology) , excitation , robustness (evolution) , exponential stability , linear system , mathematics , stability (learning theory) , convergence (economics) , work (physics) , state (computer science) , computer science , mathematical analysis , nonlinear system , physics , algorithm , biochemistry , chemistry , control (management) , quantum mechanics , artificial intelligence , machine learning , economics , gene , economic growth , thermodynamics
Summary 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, 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 nonuniform 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.