论文信息 - Stability analysis and estimate of the region of attraction of a human respiratory model

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.

[1] Wim Michiels,et al. Geometric Ideas in the Stability Analysis of Delay Models in Biosciences , 2007 .

[2] O. Santos,et al. Complete type Lyapunov-Krasovskii functionals with a given cross term in the time derivative , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3] B Vielle,et al. Delay equation analysis of human respiratory stability. , 1998, Mathematical biosciences.

[4] K. Cooke,et al. On zeroes of some transcendental equations , 1986 .

[5] L. E. El'sgolt's. Introduction to the Theory of Differential Equations with Deviating Arguments , 1966 .

[6] Silviu-Iulian Niculescu,et al. Estimates of the attraction region for a class of nonlinear time-delay systems , 2006, IMA J. Math. Control. Inf..

[7] ON COMPUTING ESTIMATES OF THE ATTRACTION REGION FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS , 2006 .

[8] V. Kharitonov,et al. Lyapunov matrices for neutral type time delay systems , 2005, 2005 2nd International Conference on Electrical and Electronics Engineering.