On Global Asymptotic Stability of SPR Adaptive Systems Without Persistent Excitation

Nikita Barabanov (1) , Romeo Ortega (2)

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

We present a sufficient condition for global asymptotic stability of linear time-varying systems of the form <(x)over dot> = Ax + B phi(inverted perpendicular)(t)theta, <(theta)over dot> = -phi(t)C-inverted perpendicular x with strictly positive real transfer function W(s) = C-inverted perpendicular(sI - A)(-1) B and the vector theta(t) not satisfying the well-known persistent excitation condition. It is also shown that the criterion is optimal in some well-defined sense-making the condition "almost" necessary as well. This class of systems arise in many control applications including system identification and adaptive control and, to the best of the authors' knowledge, no necessary and sufficient condition for global asymptotic stability has been reported.

Domaines: Automatique

Nikita Barabanov, Romeo Ortega. On Global Asymptotic Stability of SPR Adaptive Systems Without Persistent Excitation. 56th IEEE Annual Conference on Decision and Control (CDC), Dec 2017, Melbourne, Australia. ⟨10.1109/CDC.2017.8263780⟩. ⟨hal-02378402⟩