Optimal control of linear systems with parameter uncertainty

A class of infinite-horizon regulator problems is formulated for families of time-invariant linear systems with parameter uncertainty. Under a regularity assumption, the optimal linear, state-feedback control is shown to exist and is defined via a positive-definite solution of a family of Riccati-type, algebraic equations. The solvability of these equations is equivalent to the stabilizability of the family of linear systems by a constant, linear feedback.