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

Abstract

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.