A simplified linear state-space model of the ingestion of a drug in the bloodstream is given by
where
x1 = the mass of the absorbed drug in mg
x2 = the mass of the drug in the bloodstream in mg
u = the rate at which the drug is ingested in mg/min
(a) Find the state-transition matrix of the system.
(b) Obtain a discrete-time state-space model for the system with a sampling period T in terms of the model parameters.