Compactness and nuclearity of Hankel operators
In this chapter, we examine the relationships between the exponential (or strong) stability of certain classes of well-posed linear systems and the compactness and nuclearity properties of the Hankel operator. New suÆcient conditions for nuclearity are given for exponentially stable, regular, well-posed linear systems with an analytic semigroup. In the last section of this chapter w ewill derive a bound on the L ∞-error of a sub-optimal Hankel norm approximant of a system with a nuclear Hankel operator.
KeywordsTransfer Function Exponential Stability Strong Stability Analytic Semigroup Hankel Operator
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