Lyapunov stability analysis for nonlinear delay systems

Sufficient conditions ensuring that a nonlinear system with disturbances having a delay is delay independent globally asymptotically stable, are given. The proof carried out relies extensively on a characterization of the stability property in terms of the Lyapunov function. The result is applied to some biological systems and neural networks. It is also used to construct a stabilizing memoryless controller for a second order system with state-delay.

[1]  John Tsinias,et al.  Sufficient lyapunov-like conditions for stabilization , 1989, Math. Control. Signals Syst..

[2]  M. Jankovic.  Control Lyapunov-Razumikhin functions for time delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[4]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[5]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

[6]  Daniel I. Barnea.  A Method and New Results for Stability and Instability of Autonomous Functional Differential Equations , 1969 .

[7]  P. Kokotovic,et al.  Global stabilization of partially linear composite systems , 1990 .

[8]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[9]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[10]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[11]  Yuan Wang,et al.  Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability , 1996, Math. Control. Signals Syst..

[12]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[13]  J. Hopfield.  Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons , 1984 .

[14]  Jean-Pierre Richard,et al.  Nonlinear delay systems: Tools for a quantitative approach to stabilization , 1998 .

[15]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .