Stability of Multiparameter Singular Perturbation Problems with Parameter Bounds, I. Time-Varying Systems with Cone-Restricted Perturbations.

Abstract

Explicit upper bounds are obtained for the singular perturbation parameters of a general uniformly asymptotically stable multiparameter singularly perturbed system. The study focuses on the linear time-varying case studied by H. K. Khalil and P.V. Kokotovic (SIAM J. Control Opt., 17, 56-65, 1979) in which the small parameters are constrained to have bounded mutual ratios. An upper bound is obtained on a weighted norm of the vector of singular perturbation parameters such that uniform asymptotic stability is ensured if this bound is met. The derivation makes liberal use of Liapunov function arguments. In a companion paper [2], it is shown that for linear time-invariant systems the 'bounded mutual ratios' assumption can be lifted, and typically less conservative parameter estimates are obtained.