The linear quadratic regulator problem is considered, and a method for obtaining an optimal output feedback control subject to a minimax performance index is presented. The optimal constant feedback matrix, which denotes the optimal constant feedback gains, is determined by minimizing the effects of the worst value of the initial state on the system performance measure. First, the necessary conditions for a minimax solution are given analytically. However, it is very difficult to determine the minimax solution directly from these necessary conditions. Then, a method for obtaining an optimal numerical solution by using a recursive formula is presented. Two iterative algorithms for the minimax solution are given. These algorithms are based on Theorem 4 and the saddle point assumption is not used. As shown in the illustrative examples the iterative solutions converge to the minimax value rapidly, and this method is useful for obtaining the minimax output feedback solution.

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