Properties of the transfer functions of compartmental models
The author is concerned with the structure of the transfer function for a linear time-invariant state-space compartmental model. In particular, he has investigated the set of nonlinear algebraic equations that arise from the transfer function relating the unknown model parameters of the system to the known coefficients of the transfer function. These nonlinear equations possess many interesting properties, some of which have been studied here. A need for a systematic approach to analyze these properties exists. Similarly there is a need for tools to solve the equations and uncover important features they have. The author has initiated a systematic approach by establishing the form of the component function to be analyzed. Using this system the author answers some questions as for example if a given transfer function is the transfer function for some compartmental system. He proves that if the transfer function coefficients do not satisfy all the conditions of a certain proposition or theorem the answer is no. An application of these results is contained in a further theorem, in which a simple necessary condition is given for all roots of a polynomial with positive coefficients to be real and negative. Most eigenvalues of compartmental models fall into this category. Furthermore, the triangularization approach has been used by the author. He currently developed a way of finding the number of compartmental models corresponding to a given transfer function.
scientific article; zbMATH DE number 3902444