Asymptotic stability analysis of certain neutral differential equations: A descriptor system approach

Based on the descriptor and ''neutral type'' model transformation, some corresponding Lyapunov-Krasovskii functionals are introduced for stability analysis of certain neutral differential equations. Delay-dependent and delay-independent stability criteria are given in terms of linear matrix inequalities. The proposed criteria are less conservative and restrictive than other existing criteria since they are based on an equivalent neutral model transformation or parameterized transformation. Examples are given to illustrate advantages of our approach.

[1]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[2]  V. Kharitonov,et al.  On delay-dependent stability conditions ☆ , 2000 .

[3]  Stuart Townley,et al.  The effect of small delays in the feedback loop on the stability of neutral systems , 1996 .

[4]  Yuan Gong Sun,et al.  Note on asymptotic stability of a class of neutral differential equations , 2006, Appl. Math. Lett..

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

[6]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[7]  Ju H. Park,et al.  Delay-dependent criterionfor asymptotic stability of a class of neutral equations , 2004, Appl. Math. Lett..

[8]  R. Agarwal,et al.  Asymptotic stability of certain neutral differential equations , 2000 .

[9]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[10]  E. Fridman.  Stability of linear descriptor systems with delay: a Lyapunov-based approach , 2002 .

[11]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

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

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

[14]  Hassan A. El-Morshedy,et al.  Nonoscillation, oscillation and convergence of a class of neutral equations , 2000 .

[15]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[16]  K. Gopalsamy,et al.  Convergence under dynamical thresholds with delays , 1997, IEEE Trans. Neural Networks.

[17]  LiaoXiaofeng,et al.  Delay-dependent exponential stability analysis of delayed neural networks , 2002 .

[18]  Xiaofeng Liao,et al.  Global exponential stability for a class of retarded functional differential equations with applications in neural networks , 2004 .