On the Role of Passivity and Output Injection in the Output Feedback Stabilisation Problem: Application to Robot Control

Abstract

Existing dynamic output feedback stabilisation techniques of non-linear systems are applicable mainly when the unmeasurable part of the state enters linearly. Our objective in this paper is to identify a class of systems, non-linear with respect to the unmeasured variables, which are globally asymptotically stabilisable via dynamic output feedback. To achieve this characterisation we explore two routes: systems passifiability, and the combination of state feedback plus output injection. While the first line of research is motivated by the recent developments in robot control, the second one is an attempt to extend the work of the first author to the non-linear dependence case. Our contributions are twofold: first, we present a series of general theorems that identify the class mentioned above. Second, we apply these theorems to derive in a systematic manner, and using a unified framework, some recent schemes on global set point control of rigid and elastic joint robots using only position measurements.