Eigenvector approach for order reduction of singularly perturbed linear-quadratic optimal control problems

In this paper we show how to decompose the singularly perturbed algebraic R iccati equation and the corresponding linear-quadratic optimal control prob lem at steady state in terms of reduced-order pure-slow and pure-fast probl ems by using the eigenvector approach. The eigenvector approach should be u sed for decomposition of singularly perturbed control systems in the cases when the singular perturbation parameter is not very small. In such cases t he decomposition methods based on series expansions, fixed point iterations , subspace iterations, and Newton iterations, either fail to produce soluti ons of the corresponding algebraic equations or display very slow convergen ce. (C) 1999 Elsevier Science Ltd. All rights reserved.