Abstract
The optimal control of linear time-invariant systems relative to time-multiplied quadratic performance indices is discussed. The problem is posed with an additional constraint that the control vector is a linear time-invariant function of the output vector rather than of the state vector. The degree of optimality assigning a physically meaningful measure of the “quality” of control systems which are not optimal is proposed and applied to this problem.
The necessary condition for minimizing matrix of feedback gains is obtained in the form of algebraic equations. The second and fourth order systems are examined in detail as examples.
