The frequency domain solution of regulator problems

In the past, quadratic optimization problems have been examined from both the time and frequency-domain points of view but there has been little effort devoted to comparing these two approaches. The purpose of this paper is to spell out in detail how one can solve Kalman´s regulator problem in the frequency domain and to compare the forms of the equations defining the optimal compensators obtained in this way with those obtained by Kalman. In particular, the equivalence between spectral factorization and solving for the steady-state solutions of a matrix Riccati equation is established, and the frequency-domain implications of optimality are examined.