The standard ℋ2-optimal control problem: a polynomial solution

In this paper we present a solution to the ‘standard’ ℋ2 control problem. The solution presented here is based upon the algebra of polynomials, and in particular we use the polynomial equation approach. In considering the scalar version of the standard ℋ2 problem we derive a couple of linear polynomial (diophantine) equations which define the optimal regulator. The coefficients of these equations are obtained from polynomial spectral factorization.