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Abstract
Abstract Based on the matrix fraction description (MFD) consideration and polynomial matrix algebra, interesting results for the multivariable discrete linear quadratic regulator and optimal estimator are derived. The solutions are obtained by the spectral factorization of polynomial matrices in concise forms. The difficulties of solving the discrete algebraic Riccati equation can thus be avoided. In the derivation, some connections between the state space approach and the frequency domain approach are further investigated.
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