Smooth time-varying stabilization of driftless systems over communication channels

Abstract

We address the problem of smooth time-varying stabilization of port-interconnected driftless passive systems. The benchmark that we study is reminiscent of driftless systems interconnected over communication channels and constitutes a generalization of the well-known chained-form nonholonomic systems. Our contribution consists in proposing a smooth time-varying controller that guarantees uniform global asymptotic stability; moreover, a necessary condition is also stated. Both the sufficient and necessary conditions are formulated in terms of the so-called δ -persistency of excitation previously used in set-point control of nonholonomic systems. The proof of sufficiency relies on a recently reported extended Matrosov's theorem which may be regarded as an extension of Krasovskı˘i-La Salle's invariance principle to the case of nonautonomous systems.