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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.
Levine et al. (Sun,) studied this question.