In the past, Type-1 diabetes patients had to inject themselves with insulin

In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state space model matrices are given by

where the state vector is given by

The state variables are

x₁ = insulin amount in plasma compartment

x₂ = insulin amount in liver compartment

x₃ = insulin amount in interstitial (in body tissue) compartment

The system’s input is u = external insulin flow.

The system’s output is y = plasma insulin concentration.

a. Find the system’s transfer function.

b. Verify your result using MATLAB.