Several relations between the time domain and frequency domain approaches of linear quadratic optimal design

In this paper, several relations between the time domain and frequency domain approaches to linear-quadratic optimal design are derived. These relations include three parts: one is used to explain the feedback parts, the other is used to join the input signals, and another is used to bridge the disturbances of these two approaches. Moreover, we show that the system designed in the time domain is equivalent to the system designed in the frequency domain for model-following systems with output disturbance. Based on these results, the compensators or the state-feedback gain can be made the same by following the classical and modern optimal design procedures. Only single-variable systems are considered. One example is used to illustrate these results.