On the determination of the optimal constant output feedback gains for linear multivariable systems

The optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed. The problem is posed with the additional constraint that the control vector u (t) is a linear time-invariant function of the output vector y (t) (u (t) = -Fy (t) ) rather than of the state vector x (t). The performance criterion is then averaged, and algebraic necessary conditions for a minimizing F are found. In addition, an algorithm for computing F is presented.