On Solving Partially Stable L Q-Optimal Control by Spectral Factorization

This paper reports a method for solving by spectral factorization the linear quadratic optimal control of a linear time-invariant stabilizable system with i) a not completely detectable state in the output in the integral of the cost function and ii) a terminal partial stabilization constraint. The solution by state feedback has been given by Willems and Callier. The new method extends the polynomial matrix spectral factorization technique developed by Kucera for the standard LQ-regulator with stabilization constraint.