Explicit optimality conditions for fixed-order dynamic compensation

We consider steady-state, linear-quadratic fixed-order dynamic compensation in the presence of disturbance and observation noise. First-order necessary conditions for the optimization problem are derived in a new and highly simplified form. These necessary conditions constitute a system of two modified Riccati equations and two modified Lyapunov equations coupled by a projection which plays an essential role in defining the geometric structure of the compensator. When the order of the compensator is equal to the dimension of the plant, the classical linear-quadratic-Gaussian results are immediately obtained.