Stability analysis and estimate of the region of attraction of a human respiratory model

Raúl Villafuerte (1) , Sabine Mondié (1) , Silviu-Iulian Niculescu (2)

1 CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
2 L2S - Laboratoire des signaux et systèmes

In this paper, we complete the stability analysis of the human respiratory nonlinear time delay model introduced by[9]. More precisely, we present a detailed mathematical analysis of the stability of the trivial equilibrium of the nonlinear model, an estimate of its region of attraction and exponential estimates of the solutions starting in this region for two distinct control strategies linear and Hill controllers, respectively. The proposed approach is constructive and it is based on the use of Lyapunov-Krasovskii functionals of complete type for timedelay systems with a cross term in the derivative. © 2008 IEEE.

Mots clés: Control strategies; Cross terms; Exponential estimates; Lyapunov-Krasovskii functionals; Mathematical analysis; Non-linear models; Nonlinear time delays; Region of attractions; Respiratory models; Stability analysis; Time-delay systems; Trivial equilibriums; System stability; Delay control systems

Domaines: Automatique / Robotique

Raúl Villafuerte, Sabine Mondié, Silviu-Iulian Niculescu. Stability analysis and estimate of the region of attraction of a human respiratory model. 47th IEEE Conference on Decision and Control, CDC 2008, Dec 2008, Cancun, Mexico. pp.2644-2649, ⟨10.1109/CDC.2008.4738770⟩. ⟨hal-02291747⟩