Finite-Dimensional Hybrid Observer for Delayed Impulsive Model of Testosterone Regulation

The paper deals with the model-based estimation of hormone concentrations that are inaccessible for direct measurement in the blood stream. Previous research demonstrated that the dynamics of nonbasal 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.