Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters

The stochastic finite-time boundedness (FTB) problem is considered for a class of Markovian jumping neural networks (MJNNs) with time delay and uncertainties. By selecting the appropriate stochastic Lyapunov-Krasovskii functional, sufficient conditions of stochastic FTB of MJNNs are presented and proved. The FTB criteria are formulated in the form of linear matrix inequalities. Simulation results illustrate the effectiveness of the developed approaches.

[1]  Hiroyuki Ichihara,et al.  Necessary and sufficient conditions for finite-time boundedness of linear continuous-time systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  J. Lam,et al.  Global robust exponential stability analysis for interval recurrent neural networks , 2004 .

[3]  Jun Hu,et al.  Robust stability of delayed genetic regulatory networks with different sources of uncertainties , 2011 .

[4]  Francesco Amato,et al.  Input-output finite time stabilization of linear systems , 2010, Autom..

[5]  Shihua Li,et al.  Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance , 2011, Appl. Math. Comput..

[6]  Jinde Cao,et al.  Exponential synchronization of stochastic perturbed chaotic delayed neural networks , 2007, Neurocomputing.

[7]  Caixia Liu,et al.  Robust finite-time stabilization of uncertain singular Markovian jump systems , 2012 .

[8]  Magdi S. Mahmoud,et al.  Finite-time analysis and H∞ control for switched stochastic systems , 2012, J. Frankl. Inst..

[9]  Gang Feng,et al.  Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems , 2012, Autom..

[10]  Zidong Wang,et al.  On global exponential stability of generalized stochastic neural networks with mixed time-delays , 2006, Neurocomputing.

[11]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[12]  Peng Shi,et al.  Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay , 2011, Neurocomputing.

[13]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[14]  Francesco Amato,et al.  Finite-time stabilization of impulsive dynamical linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[15]  Shihua Li,et al.  Finite-time boundedness and stabilization of switched linear systems , 2010, Kybernetika.

[16]  Zidong Wang,et al.  Robust stability for stochastic Hopfield neural networks with time delays , 2006 .

[17]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[18]  P. Shi,et al.  Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays , 2007 .

[19]  Fei Liu,et al.  Finite-Time $H_{\infty}$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback , 2012, IEEE Transactions on Fuzzy Systems.

[20]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[21]  Zidong Wang,et al.  Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon , 2011, IEEE Transactions on Neural Networks.

[22]  Huijun Gao,et al.  New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays , 2010, Neurocomputing.

[23]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[24]  J. Lam,et al.  Delay-dependent exponential stability for a class of neural networks with time delays , 2005 .

[25]  Shengyuan Xu,et al.  Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks , 2011, Neurocomputing.

[26]  Xudong Zhao,et al.  Delay-dependent observer-based H∞ finite-time control for switched systems with time-varying delay , 2012 .

[27]  Shengyuan Xu,et al.  Delay-dependent stability of neutral type neural networks with distributed delays , 2009, Neurocomputing.

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