μ-stability of infinite delay functional differential systems with impulsive effects

References

• Lakshmikantham , V , Bainov , D and Simeonov , P . 1989 . Theory of Impulsive Differential Equations , Singapore : World Scientific .
   Google Scholar
• Bainov , D and Simenov , P . 1989 . Systems with Impulse Effect: Stability Theory and Applications , Chichester : Ellis Horwood Limited .
   Google Scholar
• Fu , X , Yan , B and Liu , Y . 2005 . Introduction of Impulsive Differential Systems , Beijing : Science Press .
   Google Scholar
• Stamova , I and Stamov , G . 2001 . Lyapunov-Razumikhin method for impulsive functional equations and applications to the population dynamics . J. Comput. Appl. Math. , 130 : 163 – 171 .
   Web of Science ®Google Scholar
• Ignatyev , A , Ignatyev , O and Soliman , A . 2006 . Asymptotic stability and instability of the solutions of systems with impulse action . Math. Notes , 80 : 491 – 499 .
   Web of Science ®Google Scholar
• Ignatyev , A . 2008 . On the stability of invariant sets of systems with impulse effect . Nonlinear Anal. , 69 : 53 – 72 .
   Web of Science ®Google Scholar
• Nieto , JJ and O'Regan , D . 2009 . Variational approach to impulsive differential equations . Nonlinear Anal. , 10 : 680 – 690 .
   Web of Science ®Google Scholar
• Liu , X and Ballinger , G . 2001 . Uniform asymptotic stability of impulsive delay differential equations . Comput. Math. Appl. , 41 : 903 – 915 .
   Web of Science ®Google Scholar
• Liu , X and Wang , Q . 2007 . The method of Lyapunov functionals and exponential stability of impulsive systems with time delay . Nonlinear Anal.: Theory, Methods Appl. , 66 : 1465 – 1484 .
   Web of Science ®Google Scholar
• Ahmad , B . 2009 . Stability in terms of two measures for perturbed impulsive delay integro-differential equations . Appl. Math. Comput. , 214 : 83 – 89 .
   Web of Science ®Google Scholar
• Wang , Q and Liu , X . 2007 . Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method . Appl. Math. Lett. , 20 : 839 – 845 .
   Web of Science ®Google Scholar
• Shen , J . 1996 . Existence and uniqueness of solutions for a class of infinite delay functional differential equations with applications to impulsive differential equations . J. Huaihua Teach. Coll. , 15 : 45 – 51 . (in Chinese)
   Google Scholar
• Shen , J and Yan , J . 1998 . Razumikhin type stability theorems for impulsive functional differential equations . Nonlinear Anal. , 33 : 519 – 531 .
   Web of Science ®Google Scholar
• Shen , J . 1999 . Razumikhin techniques in impulsive functional differential equations . Nonlinear Anal. , 36 : 119 – 130 .
   Web of Science ®Google Scholar
• Gimenes , L , Federson , M and Taboas , P . 2007 . Impulsive stability for systems of second order retarded differential equations . Nonlinear Anal.: Theory, Methods Appl. , 67 : 545 – 553 .
   Web of Science ®Google Scholar
• Luo , Z and Shen , J . 2001 . Stability results for functional differential equations with infinite delays . J. Comput. Appl. Math. , 131 : 55 – 64 .
   Web of Science ®Google Scholar
• Luo , Z and Shen , J . 2001 . Stability and boundedness for impulsive functional differential equations with infinite delays . Nonlinear Anal. , 46 : 475 – 493 .
   Web of Science ®Google Scholar
• Xia , Y and Wong , PJY . 2009 . Global exponential stability of a class of retarded impulsive differential equations with applications . Chaos, Solitons Fractals , 39 : 440 – 453 .
   Web of Science ®Google Scholar
• Xia , Y , Huang , Z and Han , M . 2008 . Exponential p-stability of delayed Cohen-Grossberg-type BAM neural networks with impulses . Chaos, Solitons Fractals , 38 : 806 – 818 .
   Web of Science ®Google Scholar
• Bainov , D and Stamova , I . 1995 . Uniform asymptotic stability of impulsive differential-difference equations of neutral type by Lyapunov's direct method . J. Comput. Appl. Math. , 62 : 359 – 369 .
   Web of Science ®Google Scholar
• Fu , X and Li , X . 2008 . W-stability theorems of nonlinear impulsive functional differential systems . J. Comput. Appl. Math. , 221 : 33 – 46 .
   Web of Science ®Google Scholar
• Hristova , S . 2010 . Integral stability in terms of two measures for impulsive functional differential equations . Math. Comput. Model. , 51 : 100 – 108 .
   Web of Science ®Google Scholar
• Li , X , Ding , C and Zhu , Q . 2010 . Synchronization of stochastic perturbed chaotic neural networks with mixed delays . J. Franklin Inst. , 347 : 1266 – 1280 .
   Web of Science ®Google Scholar
• Li , X . 2010 . New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays . Nonlinear Anal.: Real World Appl. , 11 : 4194 – 4201 .
   Web of Science ®Google Scholar
• Li , X , Fu , X , Balasubramaniam , P and Rakkiyappan , R . 2010 . Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations . Nonlinear Anal.: Real World Appl. , 11 : 4092 – 4108 .
   Web of Science ®Google Scholar
• Rakkiyappan , R , Balasubramaniam , P and Cao , J . 2010 . Global exponential stability results for neutral-type impulsive neural networks . Nonlinear Anal.: Real World Appl. , 11 : 122 – 130 .
   Web of Science ®Google Scholar
• Zhu , Q and Cao , J . 2010 . Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays . Neurocomputing , 73 : 2671 – 2680 .
   Web of Science ®Google Scholar
• Samidurai , R , Anthoni , S and Balachandran , K . 2010 . Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays . Nonlinear Anal.: Hybrid Syst. , 4 : 103 – 112 .
   Web of Science ®Google Scholar
• Fu , X and Li , X . 2009 . Razumikhin-type stability theorems on exponential stability of impulsive infinite delay differential systems . J. Comput. Appl. Math. , 224 : 1 – 10 .
   Web of Science ®Google Scholar
• Liu , X and Chen , T . 2008 . Robust μ-stability analysis for uncertain stochastic neural networks with unbounded time-varying delay . Physica A , 387 : 2952 – 2962 .
   Web of Science ®Google Scholar
• Li , X . 2009 . Uniform asymptotic stability and global stability of impulsive infinite delay differential equations . Nonlinear Anal.: Theory, Methods Appl. , 70 : 1975 – 1983 .
   Web of Science ®Google Scholar
• Chen , T and Wang , L . 2007 . Global μ-stability of delay neural networks with unbounded time-varying delay . IEEE Trans. Neural Netw. , 18 : 705 – 709 .
   Google Scholar