Composite control of a singularly perturbed uncertain system with slow non-linearities

Abstract

A practical stability controller for a class of non-linear singularly perturbed uncertain dynamical systems is designed using the composite control technique. The class of systems considered has non-linearities that depend upon the slow dynamics of the system. The system is uncertain in the slow dynamics as only a nominal slow behaviour is assumed to be known, together with some bound on the non-linearities. The controller guarantees practical stability in the sense that it drives the state of the system in a sufficiently small neighbourhood of the origin.