Partially stable LQ-optimal control by spectral factorization

This paper presents a method for solving by spectral factorization the linear quadratic optimal control of a linear time-invariant stabilizable system with an incompletely detectable state in the output in the integral of the cost function and a terminal partial stabilization constraint. The solution by state feedback has been given by Willems and Callier (1983). The new method extends the polynomial matrix spectral factorization technique developed by Kucera (1981) for the standard LQ-regulator with stabilization constraint. An example and several comments add perspective to the results which are mainly intended to discover the correct spectral factorization equation.