Abstract
A frequency-domain theory which is applicable to all linear systems and a class of non-linear systems is formulated in a Hilbert resolution space setting. Our approach is predicated on an ‘analytic’ characterization of certain non-selfadjoint operator algebras due to Arveson. Although originally used as an analytic tool, Arveson, in fact, formulated an operator-valued frequency response function for the elements of these algebras which, in particular, include the causal operators defined on a Hilbert resolution space. The resultant Arveson frequency response (AFR) is well defined for all linear and non-linear systems on a Hilbert resolution space and in the linear case it is characterized by an analyticity theory which is identical to that of the classical time-invariant frequency response concept. Moreover, it yields computationally viable formulae for the most widely studied classes of linear systems including the time-varying ABCD systems. Finally, the classical frequency response concepts and their ti...
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