Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result.

[1]  Bing Chen,et al.  Global Stability Criterion for Delayed Complex-Valued Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Neyir Ozcan,et al.  New global robust stability condition for uncertain neural networks with time delays , 2014, Neurocomputing.

[3]  Xinzhi Liu,et al.  Exponential stability of a class of complex-valued neural networks with time-varying delays , 2015, Neurocomputing.

[4]  Vimal Singh,et al.  On global robust stability of interval Hopfield neural networks with delay , 2007 .

[5]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Donq-Liang Lee,et al.  Relaxation of the stability condition of the complex-valued neural networks , 2001, IEEE Trans. Neural Networks.

[7]  Sabri Arik,et al.  A new condition for robust stability of uncertain neural networks with time delays , 2014, Neurocomputing.

[8]  Changyin Sun,et al.  Global Robust Exponential Stability of Interval Neural Networks with Delays , 2002, Neural Processing Letters.

[9]  Ting-Zhu Huang,et al.  Some improved criteria for global robust exponential stability of neural networks with time-varying delays , 2010 .

[10]  Xiaolin Li,et al.  New results for global robust asymptotic stability of BAM neural networks with time-varying delays , 2010, Neurocomputing.

[11]  Sabri Arik,et al.  New results for robust stability of dynamical neural networks with discrete time delays , 2010, Expert Syst. Appl..

[12]  Ligang Wu,et al.  Receding Horizon Stabilization and Disturbance Attenuation for Neural Networks With Time-Varying Delay , 2015, IEEE Transactions on Cybernetics.

[13]  Tao Zhao,et al.  Global robust exponential stability for interval neural networks with delay , 2009 .

[14]  Jinde Cao,et al.  Global robust stability of interval neural networks with multiple time-varying delays , 2007, Math. Comput. Simul..

[15]  Ruya Samli,et al.  Global robust stability analysis of uncertain neural networks with time varying delays , 2015, Neurocomputing.

[16]  Garimella Rama Murthy,et al.  Global Dynamics of a Class of Complex Valued Neural Networks , 2008, Int. J. Neural Syst..

[17]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.

[18]  Zhigang Zeng,et al.  Multistability of Two Kinds of Recurrent Neural Networks With Activation Functions Symmetrical About the Origin on the Phase Plane , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Wei Zhang,et al.  Global robust stability of complex-valued recurrent neural networks with time-delays and uncertainties , 2014 .

[20]  Jinde Cao,et al.  Nonlinear Measure Approach for the Stability Analysis of Complex-Valued Neural Networks , 2015, Neural Processing Letters.

[21]  Zhenjiang Zhao,et al.  Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays , 2016, Neural Networks.

[22]  Qiankun Song,et al.  Boundedness and Complete Stability of Complex-Valued Neural Networks With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Sabri Arik,et al.  A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks , 2013, Neural Networks.

[24]  Ting-Zhu Huang,et al.  Improved global robust exponential stability criteria for interval neural networks with time-varying delays , 2011, Expert Syst. Appl..

[25]  Zhenjiang Zhao,et al.  Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays , 2015, Neurocomputing.

[26]  Tingzhu Huang,et al.  Further analysis on global robust exponential stability of neural networks with time-varying delays , 2012 .

[27]  Jinde Cao,et al.  Global robust stability of delayed recurrent neural networks , 2004 .

[28]  Neyir Ozcan,et al.  A New Sufficient Condition for Global Robust Stability of Delayed Neural Networks , 2011, Neural Processing Letters.

[29]  Jian Chen,et al.  Further stability analysis for delayed complex-valued recurrent neural networks , 2017, Neurocomputing.

[30]  Jinde Cao,et al.  Novel results concerning global robust stability of delayed neural networks , 2006 .

[31]  Sanyi Tang,et al.  Robust stability analysis of impulsive complex-valued neural networks with time delays and parameter uncertainties , 2017, Journal of Inequalities and Applications.

[32]  Zhenjiang Zhao,et al.  Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects , 2016, Neural Networks.

[33]  Eylem Yucel.  An analysis of global robust stability of delayed dynamical neural networks , 2015 .

[34]  Tianping Chen,et al.  Robust global exponential stability of Cohen-Grossberg neural networks with time delays , 2004, IEEE Transactions on Neural Networks.

[35]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[36]  Jacek M. Zurada,et al.  Complex-valued multistate neural associative memory , 1996, IEEE Trans. Neural Networks.

[37]  Ruya Samli,et al.  A new delay-independent condition for global robust stability of neural networks with time delays , 2015, Neural Networks.

[38]  Libin Rong.  LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[39]  Jun Wang,et al.  Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Tianping Chen,et al.  Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Zhenjiang Zhao,et al.  Stability analysis of complex-valued neural networks with probabilistic time-varying delays , 2015, Neurocomputing.

[42]  Qing Zhu,et al.  New results of global robust exponential stability of neural networks with delays , 2010 .

[43]  Sabri Arik,et al.  Robust stability analysis of a class of neural networks with discrete time delays , 2012, Neural Networks.

[44]  Hamid Reza Karimi,et al.  Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ – $l_{\infty }$ Performances , 2017, IEEE Transactions on Cybernetics.