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.
Type de document :
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

Citation

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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