An Example of State-Variable Analysis from Physiology and Medicine

The state-variable approach to linear system analysis is applied to an example problem originating in the fields of physiology and medicine. A linear, time-invariant model is formulated to describe the absorption of an orally administered drug into the bloodstream from the gastrointestinal tract, and the subsequent removal of the drug from the bloodstream by the passive clearance function of the kidneys. Although the model presented is much simplified from the physiological standpoint, it suffices to highlight the type of information obtainable from the state-variable analysis.