Optimality with input derivatives

Optimal control of the linear system containing input derivatives is formulated using transformed co-ordinates. The transformation introduces crossproduct weighting into the quadratic performance index and leads to an additional feedback control component which can be related to a direct least-squares minimisation. In the frequency domain, the overall system return-difference matrix is shown to include a transformation related to the inverse of other return-difference matrices associated with the components of the transformed input driving matrix.