# American Institute of Mathematical Sciences

September  2009, 12(2): 455-468. doi: 10.3934/dcdsb.2009.12.455

## Robust closed-loop control of plasma glycemia: A discrete-delay model approach

 1 Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", Consiglio Nazionale delle Ricerche (IASI-CNR), Viale Manzoni 30, 00185 Roma, Italy 2 Dipartimento di Ingegneria Elettrica e dell'Informazione, Università degli Studi dell'Aquila, 67040 Poggio di Roio, L'Aquila, Italy 3 Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", Consiglio Nazionale delle Ricerche (IASI-CNR), BioMatLab - UCSC - Largo A. Gemelli 8, 00168 Roma, Italy

Received  November 2008 Published  July 2009

The paper investigates the problem of tracking a desired plasma glucose evolution by means of intra-venous insulin administration. A model-based approach is followed. A recent model of the glucose/insulin regulatory system which consists of discrete-delay nonlinear differential equations is used. A disturbance is added to the insulin kinetics in order to model uncertainties concerning both the insulin delivery rate and the mechanism actuating the insulin pump. A feedback control law which yields input-to-state stability of the closed loop error system with respect to the disturbance is provided. Such control law depends on the glucose and insulin measurements at the present and at a delayed time. In silico simulations validate the theoretical results.
Citation: Pasquale Palumbo, Pierdomenico Pepe, Simona Panunzi, Andrea De Gaetano. Robust closed-loop control of plasma glycemia: A discrete-delay model approach. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 455-468. doi: 10.3934/dcdsb.2009.12.455
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