Input-to-state stability analysis of impulsive stochastic neural networks based on average impulsive interval

This paper addresses the input-to-state stability (ISS) properties, including pth moment ISS (p-ISS) and stochastic ISS (SISS) for a class of impulsive stochastic neural networks with external inputs. Employing Lyapunov functions and stochastic analysis techniques, sufficient conditions in forms of linear matrix inequalities for the p-ISS and SISS are established based on the average impulsive interval concept. Moreover, a criterion on the pth moment globally asymptotic stability and globally asymptotic stability in probability is derived as a corollary. Finally, an example is provided to illustrate the effectiveness of the obtained results.

[1]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[2]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[3]  Mohamad H. Hassoun,et al.  Recurrent neural nets as dynamical Boolean systems with application to associative memory , 1997, IEEE Trans. Neural Networks.

[4]  Vijayan K. Asari,et al.  Recurrent neural network as a linear attractor for pattern association , 2006, IEEE Transactions on Neural Networks.

[5]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[6]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[7]  Pierdomenico Pepe,et al.  Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability , 2008, IEEE Transactions on Automatic Control.

[8]  Choon Ki Ahn,et al.  Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay , 2010, Inf. Sci..

[9]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[10]  Jinde Cao,et al.  Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches , 2011, Neural Networks.

[11]  Yu Kang,et al.  Stochastic input-to-state stability of switched stochastic nonlinear systems , 2012, Autom..

[12]  Song Zhu,et al.  Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays , 2013, Neural Computing and Applications.

[13]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[14]  Choon Ki Ahn.  An input-to-state stability approach to filter design for neural networks with noise disturbance , 2012 .

[15]  Tingwen Huang,et al.  Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays , 2013, Cognitive Neurodynamics.

[16]  Jinde Cao,et al.  Mean-square exponential input-to-state stability of stochastic delayed neural networks , 2014, Neurocomputing.

[17]  Hao Shen,et al.  On input-to-state stability of impulsive stochastic systems , 2014, J. Frankl. Inst..

[18]  Yong Xu,et al.  Mean square input-to-state stability of a general class of stochastic recurrent neural networks with Markovian switching , 2014, Neural Computing and Applications.

[19]  Jinde Cao,et al.  Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays , 2014, Nonlinear Dynamics.

[20]  Weisong Zhou,et al.  Mean-square exponentially input-to-state stability of stochastic Cohen-Grossberg neural networks with time-varying delays , 2015, Neurocomputing.