An alternate numerical solution to the linear quadratic problem

This note proposes a new method, based on convex programming, for solving the linear quadratic problem (LQP) directly on the parameter space generated by the feedback control gain. All stabilizing controllers are mapped into a convex set; the problem is then formulated as a minimization of a linear function over this convex set. Its optimal solution furnishes, under certain conditions, the same feedback control gain obtained from the classical Riccati equation. Generalizations to decentralized control and output feedback control design are included. The theory is illustrated by some numerical examples