Stochastic finite-time stability analysis of Markovian jumping neural networks with mixed time delays

The stochastic finite-time stability is studied in this paper for Markovian jumping neural networks with discrete and distributed delays. By defining a proper stochastic Lyapunov functional with mode-dependent Lyapunov matrices, a sufficient condition is derived such that the delayed Markovian jumping neural network under consideration is stochastically finite-time stable with respect to prescribed scalars. The stability criterion is delay- and mode-dependent, and can be readily checked by resorting to available algorithms. Two numerical examples are finally provided to show the application of the developed theory.

[1]  Jun Cheng,et al.  Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays , 2014, Appl. Math. Comput..

[2]  Fang Liu,et al.  Exponential Stability Analysis for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  R. Rakkiyappan,et al.  Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays , 2009 .

[4]  Peng Shi,et al.  Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps , 2015, Neurocomputing.

[5]  Ju H. Park,et al.  Analysis on delay-dependent stability for neural networks with time-varying delays , 2013, Neurocomputing.

[6]  Qing Lu,et al.  Robust finite-time state estimation of uncertain neural networks with Markovian jump parameters , 2015, Neurocomputing.

[7]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[8]  A. Skorokhod.  Asymptotic Methods in the Theory of Stochastic Differential Equations , 2008 .

[9]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  Qian Ma,et al.  Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities , 2011, Neurocomputing.

[11]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[12]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[14]  Daniel W. C. Ho,et al.  Robust stability of stochastic delayed additive neural networks with Markovian switching , 2007, Neural Networks.

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

[16]  Huijun Gao,et al.  Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks With Defective Statistics of Modes Transitions , 2011, IEEE Transactions on Neural Networks.

[17]  Peng Shi,et al.  Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays , 2012, Expert Syst. Appl..

[18]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

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

[20]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[21]  Matevž Kovačič,et al.  Timetable construction with Markovian neural network , 1993 .

[22]  Zhigang Zeng,et al.  Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , 2006, Neural Networks.

[23]  Short-time stability , 1961, IRE Transactions on Automatic Control.

[24]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[25]  Fei Liu,et al.  Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities , 2011 .

[26]  Yang Tang,et al.  Stability analysis of switched stochastic neural networks with time-varying delays , 2014, Neural Networks.

[27]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.

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

[29]  Piyapong Niamsup,et al.  Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks , 2015, Neurocomputing.