Abstract
It is well known that the optimization design for a linear system with quadratic performance index may be attained through the solution of the Riccati equation. In practical systems, it sometimes becomes very laborious and difficult to work out the solution, especially when the capacities of computers are limited. Kokotovic's method of singular perturbation may be considered to be suitable for these complex systems. The authors have extended this method to include higher order perturbation terms in order to improve the accuracy and proposed a mixed order perturbation method, considering the fact that the higher order terms do not necessarily contribute to the purpose.
