On-three time scale analysis

For a three-time scale system, a decomposition technique is proposed to decouple the original system into a "slow," "fast 1," and "fast 2" (faster than fast 1) subsystems. The technique involves block diagonalization using three-stage linear transformations. A numerical algorithm is presented to solve the resulting Riccati type equations. A 9th order example is provided to illustrate the proposed technique.