Singular perturbations of systems controlled by energy-speed-gradient method

Existing results on partial stability of differential form of speed-gradient control for singularly perturbed systems are extended to the case of speed-gradient control in finite form. The results are illustrated by example of energy and synchronization control of two coupled pendulums, taking into account inertia of the motor. It is shown that the perturbations stemming from inertia of the coupling link and the perturbations stemming from inertia of the motor provide different influence upon the perturbed system behavior.