Abstract
Some new relations between the weighting coefficients of performance index and the feedback coefficients of the constructed system, in the standard form of single-input linear constant optimal control problems, are described. The standard form means that the plant is expressed in the phase-variable canonical form and the weighting matrix of the performance index is diagonal. The results are as follows:
1) A technique to transform the general single-input problems into the standard form is presented. In the standard form the problem of solving the algebraic matrix Riccati equation becomes the problem of solving only an n th-order algebraic equation.
2) The fact that, in the standard form, the feedback coefficients of the constructed system are always nonnegative is shown.
3) And the fact that the feedback coefficients of the constructed system are monotone increasing functions of the weighting coefficients is proved.
