Similarity Transformation Approach to Identifiability Analysis of Nonlinear Compartmental Models SANDOR VAJDA Department of Biomathematical Sciences, Mount Sinai School of Medicine, New York, New York 10029 and Department of Chemistry, Princeton University, Princeton, New Jersey 08544 KEITH R. GODFREY Department of Engineering, University of Warwick, Coventty, CV4 7AL, England zyxwvutsrqponmlkjihgf AND HERSCHEL RABITZ Department of Chemistry, Princeton University, Princeton, New Jersey 08544 Received 8 Februav 1988; revised 4 Augurt 1988 ABSTRACT Through use of the local state isomorphism theorem instead of the algebraic equiva- lence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions. zyxwvutsrqponmlkjihgfedcbaZYXWVUT 1. INTRODUCTION The analysis of structural identifiability is well established for linear, time-invariant models (see, for example, [6, 7, 12, 13, 31]), and although the tests can become tedious for complex models, there exist several finitely verifiable sufficient and necessary conditions both for local identifiability and for global identifiability. MATHEMATICAL BIOSCIENCES 93:217-248 (1989) Wlsevier Science Publishing Co., Inc., 1989 217 655 Avenue of the Americas, New York, NY 10010 0025-5564/89/$03.50