Identification and Control in Linear Compartmental Analysis

Abstract

Let us recall the general equations for a linear compartmental model:

$$ \begin{array}{*{20}{c}} {\dot x = \sum {{k_{ji}}{x_j},} }&{i = 1, \ldots ,n} \\ {{x_i}\left( 0 \right) = {\alpha _i}}&{} \end{array} $$

((2.1))

which are associated with n compartments, all connected in both directions. These compartmental models are very useful for studying drug kinetics in human or animal organisms. For example, compartmental models such as the following are relevant to beta-blockers, which are drugs that act on the blood pressure and heart rate.