Duality theory for MIMO robust disturbance rejection

Banach space duality theory is used to characterize the solutions of a nonstandard H^∞ optimization problem which is shown to be allpass in general and unique in the single-input single-output (SISO) ease. The theory leads to a numerical solution of duality and convex optimization, which is applied to an example. For a limiting case of sharp cutoff filters, an explicit solution of the optimal robust disturbance attenuation problem (ORDAP) resembling the two arc theorem of complex analysis is derived