Return difference bode diagram for optimal system design

This paper is concerned with a graphical method for the determination of bandwidth and optimal feedback gains for linear systems employing a quadratic form performing index. Using a fundamental frequency-domain condition of optimality developed by R. E. Kalman [1], the gain and bandwidth estimates are found from a logarithmic amplitude vs. frequency plot of the optimal system return difference. The method can be extended to systems with multiple outputs. An attempt is made to provide some insight into the connection between classical and optimal design, and into the price of optimality in terms of bandwidth.