Controller Design for Uncertain Systems via Lyapunov Functions

We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov functions. The uncertainties, which are deterministic, are characterized by certain structural conditions and known bounds. As a consequence of the Lyapunov approach, the methodology is not restricted to linear systems. The robustness of these controllers in the presence of singular perturbations is considered. The situation in which the full state of the system is not available for measurement is also considered. These controllers are illustrated by application to the tracking control of a Manutec r3 robot which has an uncertain payload.