## System Identification of Models Exhibiting Exponential, Harmonic and Resonant Modes

##### Abstract

A classical problem arising in compartmental analysis is the so called identification problem or the inverse problem. One is presented with the linear time invariant compartmental model
[see pdf for notation]
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Where A is a square matrix and the dimensions of B and C are consistent with that of A. The problem is to estimate a certain subset of the matrix elements [see pdf for notation], [see pdf for notation] and [see pdf for notation] from discrete observations of the input vector u(t) and the
output vector y(t). When instantaneous mixing is assumed the analogous equations (1.1) are replaced by
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An intermediate problem is that of identifying the respective impulse response matrix i. e the matrix [see pdf for notation].