Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays

In this paper, a class of uncertain neural networks with discrete interval and distributed time-varying delays and Markovian jumping parameters (MJPs) are carried out. The Markovian jumping parameters are modeled as a continuous-time, finite-state Markov chain. By using the Lyapunov-Krasovskii functionals (LKFs) and linear matrix inequality technique, some new delay-dependent criteria is derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show the less conservativeness.

[1]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays , 2011 .

[2]  M. Ali.  Stability analysis of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time varying delays , 2014 .

[3]  Yonggang Chen,et al.  Novel delay-dependent stability criteria of neural networks with time-varying delay , 2009, Neurocomputing.

[4]  M. Syed Ali,et al.  Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays , 2011, Math. Comput. Model..

[5]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

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

[7]  Ju H. Park,et al.  A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays , 2013, Neurocomputing.

[8]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[9]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[10]  R. Rakkiyappan,et al.  Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters , 2014 .

[11]  Min Wu,et al.  Novel stability criteria for recurrent neural networks with time-varying delay , 2014, Neurocomputing.

[12]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[13]  Lin Zhao,et al.  Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays , 2009, Neurocomputing.

[14]  M. Syed Ali,et al.  Novel delay-dependent robust H∞ control of uncertain systems with distributed time-varying delays , 2014, Appl. Math. Comput..

[15]  Dan Zhang,et al.  Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays , 2012, Neural Networks.

[16]  Junzhi Yu,et al.  Global stability analysis of fractional-order Hopfield neural networks with time delay , 2015, Neurocomputing.

[17]  M. Syed Ali,et al.  Robust stability analysis of Takagi—Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays , 2011 .

[18]  Jinde Cao,et al.  Stability of Markovian jump neural networks with impulse control and time varying delays , 2012 .

[19]  M. Syed Ali,et al.  Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays , 2015, Neurocomputing.

[20]  Xiaofeng Liao,et al.  Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays , 2012, Cognitive Neurodynamics.

[21]  Peter Tiño,et al.  Markovian architectural bias of recurrent neural networks , 2004, IEEE Transactions on Neural Networks.

[22]  Zidong Wang,et al.  State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays ☆ , 2008 .

[23]  Hongjie Li,et al.  Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling , 2014, Neurocomputing.

[24]  P. Balasubramaniam,et al.  Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays , 2012 .

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

[26]  R. Rakkiyappan,et al.  Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control , 2014, Neurocomputing.

[27]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays , 2009 .

[28]  Yonggui Kao,et al.  Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates , 2014, Appl. Math. Comput..

[29]  M. Ali,et al.  Improved delay-dependent robust H∞ control of an uncertain stochastic system with interval time-varying and distributed delays , 2014 .

[30]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

[31]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[32]  Shouming Zhong,et al.  Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays , 2014, Neurocomputing.

[33]  Ju H. Park,et al.  New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays , 2008, Appl. Math. Comput..

[34]  Huabin Chen,et al.  New delay-dependent stability criteria for uncertain stochastic neural networks with discrete interval and distributed delays , 2013, Neurocomputing.

[35]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[36]  J. Qiu,et al.  New robust stability criteria for uncertain neural networks with interval time-varying delays , 2009 .

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

[38]  Shouming Zhong,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components , 2012 .

[39]  Hongyi Li,et al.  Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters , 2008 .

[40]  S. M. Lee,et al.  On robust stability for uncertain neural networks with interval time-varying delays , 2008 .