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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 190463, 12 pages
http://dx.doi.org/10.1155/2015/190463
Research Article

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

1Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg 198504, Russia
2Information Technology, Uppsala University, 75105 Uppsala, Sweden

Received 4 June 2015; Revised 19 October 2015; Accepted 20 October 2015

Academic Editor: Yan-Wu Wang

Copyright © 2015 Diana Yamalova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.