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 Juc, 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 Jucare obtained. Finally, for each result in this paper an upper bound on the perturbation parameter ε is provided under which the result is valid.