H Infinity Sensitivity Minimization for Delay Systems. Part 2.

Abstract : We have presented the solution to the simplest meaningful H (infinity) minimal weighted sensitivity problem for the case of a plant having a delay at the input. Parallel solutions are detailed in (Flamm 1986) for more general rational weighting functions, and for plants having right half plane poles and zeros in addition to the input delay. The basic techniques are essentially generalizations of those presented here with modifications made for right half plane poles and zeros in the plant. However, in the most general case, when W(s) results in a non-compact operator on H (infinity), we are not necessarily able to construct an optimal sensitivity, although we know from the theory of Sarason that one exists. We are able to 'slightly' modify any given W(s) so as to make the corresponding operator compact, and thus obtain a solution to a 'close' problem. See (Flamm 1986) for details. Areas for future work include completing the picture for the non-compact case, computational issues for the case of general weighting functions, and extensions to plants with other non-rational transfer functions. (Author)