H∞ Tools for Electrical Engineers
This chapter reviews the necessary H∞ theory. The presentation is aimed at electrical engineers with the goal of matching the mathematical results to a corresponding physical meaning. For example, a lumped, lossless 2-port admits a scattering matrix S(p) in H∞ that is real, rational, and lossless. The converse is true and the mapping from S(p) to an actual circuit via the Foster or Cauer expansions is a time-honored torment of the undergraduate electrical engineers. Suppose now thatS(p) belongs to H∞ and is lossless. Then S(p) is rational if and only if S(p) is continuous. Consequently, continuity is equivalent to the lossless 2-port being constructed from lumped elements.
KeywordsUnit Ball Half Plane Toeplitz Operator Hankel Operator Open Unit Disk
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