A singular perturbation method may be classified as a sub-optimum method of linear regulators. In the previous paper, it was proposed to adopt the repeated perturbation method with plural parameters in order to decrese the calculational labor. But the method applied only in problems of a limited scope, because the existence conditions had not been fully known.In the present paper, certain conditions for the existence of the sub-optimal solution are derived and utilized to enlarge the number of problems solvable by this method. These conditions are simpler than those given by Kokotovic et al.. The design procedure developed in this paper is also easier than conventional ones, because the suboptimal solution is obtained by the decomposition of a high-order problem into several low-order problems whose solutions are obtained independently.
A decomposition method may be classified as near-optimization method of linear regulators with small parameters. To increase the accuracy of approximation, it might be recommended to increase the order of the unperturbed system; but it will require a tedious and laborious calculation. A method, the so-called "repeated-decomposition" is developed to circumvent the difficulty. This is composed of iterations of decompositions in the expanded unperturbed systems. The repeated-decomposition method will have less calculation keeping the same degree of approximation.
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