A geometric-series approach is used to approximate the exponentials of Hamiltonian matrices for quadratic synthesis problems. The approximants of the discretized transition matrices are then used to construct piecewise-constant gains and piecewise-time varying gains for approximating a time-varying optimal gain and a time-varying Kalman gain. The proposed method is more accurate and computationally faster than those existing methods which use the Walsh function approach and the block-pulse function approach.

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