Structural properties of a flexible-joint robot model with output controllers and some related applications

This paper considers some structural properties of an n-degree-of-freedom flexible-joint robot with a simple stabilizing output controller. It is well known that, in a nonlinear system, global asymptotic stability does not necessarily imply local exponential stability, while the latter property provides an essential tool in studying various control problems. This study shows that for the model under consideration, global asymptotic stability implies local exponential stability. Applications of this result to the topic of small-signal finite-gain L-p stability and to the analysis of the perturbed system are considered. Finally, we show how a local stabilizing controller which is based on position measurements only can be integrated into a strategy that ensures, under some conditions of system uncertainty, set-point regulation (in the global sense) of an uncertain flexible-joint robot. Simulation results, which demonstrate the applications of a control scheme that is presented in this study, are included.