A linear, time-invariant model of the hypothalamic pituitary-adrenal axis of the endocrine system with five state variables

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A linear, time-invariant model of the hypothalamic pituitary-adrenal axis of the endocrine system with five state variables has been proposed as follows (Kyrylov, 2005):

where each of the state variables represents circulatory concentrations as follows:

x0 = corticotropin-releasing hormone

x1 = corticotropin

x2 = free cortisol

x3 = albumin-bound cortisol

x4 = corticosteroid-binding globulin

d0 = an external generating factor

Express the system in the form ẋ = Ax + Bu.

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