On-three time scale analysis

Abstract

In the present consideration of a three-timescale system, a block diagonalization employing three-stage linear transformations is used to decouple the original system into slow, fast, and faster subsystems. A numerical algorithm is given to solve the resulting Ricatti-type equations, and the technique is verified for the case of a ninth-order example. The technique yields substantial computational requirment reductions, since it involves subsystems that are of a lower order than the original system.