On global asymptotic stability of $\dot x = \phi(t)\phi^\top (t)x$ with $\phi(t)$ bounded and not persistently exciting

Abstract : We study global convergence to zero of the solutions of the th order differential equation . We are interested in the case when the vector is not persistently exciting, which is a necessary and sufficient condition for global exponential stability. In particular, we establish new necessary conditions on for global asymptotic stability of the zero equilibrium of the “unexcited” system. A new sufficient condition, that is strictly weaker than the ones reported in the literature, is also established. Unfortunately, it is also shown that this condition is not necessary.
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Article dans une revue
Systems and Control Letters, Elsevier, 2017, 109, pp.24-27. 〈10.1016/j.sysconle.2017.09.005〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01816386
Contributeur : Myriam Baverel <>
Soumis le : vendredi 15 juin 2018 - 11:13:00
Dernière modification le : vendredi 9 novembre 2018 - 11:50:09

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N.E. Barabanov, Roméo Ortega. On global asymptotic stability of $\dot x = \phi(t)\phi^\top (t)x$ with $\phi(t)$ bounded and not persistently exciting. Systems and Control Letters, Elsevier, 2017, 109, pp.24-27. 〈10.1016/j.sysconle.2017.09.005〉. 〈hal-01816386〉

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