A GEOMETRIC APPROACH TO NONLINEAR SINGULARLY PERTURBED CONTROL-SYSTEMS

Applications of two-time-scale singular perturbation methods have been limited to the class of models appearing in a 'standard form'. Many nonlinear control systems, such as models of aircraft and robotic manipulators with flexible joints, are two-time-scale systems, but do not appear in the standard form. The main result of this paper is a coordinate-free characterization of time-scales in terms of invariant manifolds which express conservation and equilibrium properties of the control system. A procedure for finding slow and fast states is given. Previously developed slow-fast composite control designs are thus made applicable to a wider class of nonlinear systems.