Stabilization and regulation of nonlinear singularly perturbed systems--Composite control

For a general class of nonlinear singularly perturbed systems, a two-time-scale analysis and design procedure for stabilization and regulation is presented. It is shown that, under a set of conditions, the composite control proposed by Chow and Kokotovic [5], asymptotically stabilizes the desired equilibrium and produces a finite cost J
uc
, which tends to the cost of the slow regulator as the perturbation parameter ε tends to zero. Thus, the well-posedness of the full regulator problem is established. Furthermore, under different stability requirements on the fast subsystem, explicit upper and lower bounds on J
uc
are obtained. Finally, for each result in this paper an upper bound on the perturbation parameter ε is provided under which the result is valid.