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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https://hal-centralesupelec.archives-ouvertes.fr/hal-01816386
Contributor : Myriam Baverel <>
Submitted on : Friday, June 15, 2018 - 11:13:00 AM
Last modification on : Friday, November 9, 2018 - 11:50:09 AM

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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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