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

Nikita E. Barabanov (1) , Roméo Ortega (2)

1 NDSU - North Dakota State University
2 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Automatique; Automatique / Robotique

Nikita 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, 2017, 109, pp.24-27. ⟨10.1016/j.sysconle.2017.09.005⟩. ⟨hal-01816386⟩