New results on the inverse-system/deconvolution problem for linear dynamical systems

A new theory and realization methodology for the inverse-system/deconvoluti on problem associated with dynamical systems is developed. This new theory, based on the assumption of a finite-dimensional, linearized dynamical syst em and uncertain input signals s(t) that have a feature called waveform str ucture, effectively overcomes the longstanding difficulties of realizing in verse systems for linear systems that have "more poles than zeros" and/or h ave "zeros in the right half-plane". The results obtained here are derived for both continuous and discrete-time linear systems, using either analog o r digital signal processing, and include rime-varying systems with uncertai n vector input signals s(t) = (s(1)(t),..., s(r)(t)) and/or vector output m easurements y(t) = (y(1)(t),..., y(m)(t)).