Observations on some commonly used methods for identification of parameters in linear systems

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Abstract
This paper describes and compares the application of two alternative approaches to the identification of linear systems from input-output data. The first approach is based on fitting input and output data by sums of exponentials and deriving both the system structure and the parameter values from the resulting functions. The second approach is based on assuming a differential-equation structure and finding only the parameter values from the given data. The relative advantages, disadvantages, and computational aspects of both approaches are discussed with reference to a specific biological problem. The results are applicable to a variety of engineering and scientific problems described by systems of first-order linear differential equations.