State estimation in a delayed impulsive model of testosterone regulation by a finite-dimensional hybrid observer

The paper deals with the model-based estimation of hormone concentrations that are unaccessible for direct measurement in the blood stream. Previous research demonstrated that the dynamics of non-basal endocrine regulation can be closely captured by linear continuous models with time delays under a pulse-modulated feedback. The presence of continuous time delays is inevitable in such a model due to transport phenomena and the time necessary for an endocrine gland to produce a certain hormone quantity. Yet, thanks to the Finite-Dimensional reducibility of the linear time-delay part of the system, a finite-dimensional model can be used to reconstruct both the continuous and discrete states of the hybrid time-delay plant. A hybrid observer exploiting this possibility is suggested and analyzed by means of a discrete impulse-to-impulse mapping.