On the stability of nonlinear systems with leakage delay

Abstract This paper studies uniqueness and stability of the equilibrium points of nonlinear time-delay systems with leakage delay by using the appropriate model transformation that shifts the considered systems into the neutral-type time-delay systems. Delay-independent sufficient conditions for uniqueness and delay-dependent sufficient conditions for stability are derived, respectively, by using contraction mapping theorem and suitable degenerate Lyapuniv–Krasvovskii functional together with some differential inequalities and LMI technique.

[1]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[2]  K. Gopalsamy.  Leakage delays in BAM , 2007 .

[3]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[4]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[5]  X Mao.  Exponential stability of nonlinear differential delay equations , 1996 .

[6]  Emilia Fridman,et al.  Special issue on time‐delay systems , 2003 .

[7]  L. Berezansky,et al.  On stability of some linear and nonlinear delay differential equations , 2006 .

[8]  Bart Kosko,et al.  Neural networks and fuzzy systems , 1998 .

[9]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[10]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[11]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[12]  J. Craggs.  Applied Mathematical Sciences , 1973 .

[13]  Wim Michiels,et al.  Stabilization of time-delay systems with a Controlled time-varying delay and applications , 2005, IEEE Transactions on Automatic Control.

[14]  Vimal Singh,et al.  LMI approach to the global robust stability of a larger class of neural networks with delay , 2007 .

[15]  Leonid Mirkin,et al.  H∞ control of system with I/O delay: a review of some problem‐oriented methods , 2002 .

[16]  Chaouki T. Abdallah,et al.  Time Delay Systems , 2002 .

[17]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[18]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[19]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .