Modal analysis of identifiablity of linear compartmental models

A method for analysing the structural identifiability of linear, time-invariant compartmental models in terms of normal modes is presented and applied to several examples. The equations to be examined are linear or bilinear, whereas previous methods have produced nonlinear equations. In consequence, the proposed method has the advantage that is possible to check relatively easily, by a process readily computerised, whether a unique solution exists. Also, if a proposed experiment does not result in a unique solution, it is clear how the model or the experiment must be modified to achieve this.

[1]  K. Glover,et al.  Identifiability of linear and nonlinear dynamical systems , 1976 .

[2]  J J DiStefano,et al.  Parameter identifiability and experiment design: thyroid hormone metabolism parameters. , 1977, The American journal of physiology.

[3]  J. Reid,et al.  Structural identifiability in linear time invariant systems , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[4]  Ioan Doré Landau,et al.  Reduced order bilinear models for distillation columns , 1978, Autom..

[5]  R R Mohler,et al.  Necessary and sufficient conditions in the tracer determination of compartmental system order. , 1976, Journal of theoretical biology.

[6]  S. I. Rubinow,et al.  Compartment analysis: An inverse problem , 1971 .

[7]  E. Walter,et al.  On the identifiability of linear state systems , 1976 .

[8]  Claudio Cobelli,et al.  Identifiability of compartmental systems and related structural properties , 1979 .

[9]  Joseph J. DiStefano,et al.  On the relationships between structural identifiability and the controllability, observability properties , 1977 .

[10]  Jack B. Waide,et al.  A Linear Systems Analysis of the Calcium Cycle in a Forested Watershed Ecosystem , 1974 .

[11]  M. Milanese,et al.  Structural identifiability of compartmental models and pathophysiological information from the kinetics of drugs , 1975 .

[12]  Eric Walter,et al.  Comments on "Identifiability of linear and nonlinear dynamical systems" , 1979 .

[13]  C. Cobelli,et al.  On the structural identifiability of biological compartmental systems in a general input-output configuration , 1976 .

[14]  R. Bellman,et al.  On structural identifiability , 1970 .

[15]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[16]  Claudio Cobelli,et al.  Chapter 10 – STRUCTURAL IDENTIFIABILITY OF LINEAR COMPARTMENTAL MODELS , 1979 .