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

In this paper, we complete the stability analysis of the human respiratory nonlinear time delay model introduced by (B. Vielle et al., 1998). 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.