Pseudorational functions and H/sup ∞/ theory

Y. Yamamoto, A. Tannenbaum
Proceedings of 1994 American Control Conference - ACC '94  
The H" optimization problem for a class of distributed parameter systems is studied. This class is called pseudorational, and is particularly in close relationship with Sarason's interpolation theorem. A general state space representation for Sarason's theorem is obtained. It is shown that for the case of the plant represented by a Blaschke product in this class, the optimal sensitivity computation is reduced to the limiting case of the Nevanlinna-Pick solutions. Notation and ConveFtions As
more » ... ConveFtions As usual, L[$](s) or $(s) denotes the Laplace transform of $. The Laplace transforms will always be considered to be two-sided, i.e., taken over all real line (-oo,oo). If X is a space of functions on the real line, then the space consisting of the Laplace transforms of e1:ments in X, provided they exist, is denoted by X. Let L'[O,oo) and L'(-oo,O] be the standard Lebesgue square integrable spaces: Then their Laplace transformed spaces are H ' = L'[O,oo),
doi:10.1109/acc.1994.752339 fatcat:2ywxtn4itfcthhfp6dvbrfri5m