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\ast
are found. In addition, an algorithm for computing
F\ast
is presented.