Approximate feedback design for a class of singularly perturbed systems

Approximate feedback design of a class of singularly perturbed linear regulators is developed. Two perturbation parameters are introduced, in particular, to account for the degree of smallness and extent of largeness of two boundary modes with respect to the normal mode of operation. An approximation is employed to separate the overall design into three regions. An index of suboptimality is also derived. A 9th order example is worked out to illustrate the theoretical analysis.