Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.

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

[2]  Yurong Liu,et al.  On Synchronization of Discrete-Time Markovian Jumping Stochastic Complex Networks with Mode-Dependent Mixed Time-Delays , 2009 .

[3]  Indra Gunawan,et al.  Reliability analysis of shuffle-exchange network systems , 2008, Reliab. Eng. Syst. Saf..

[4]  Zidong Wang,et al.  Global Synchronization Control of General Delayed Discrete-Time Networks With Stochastic Coupling and Disturbances , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Zidong Wang,et al.  Design of exponential state estimators for neural networks with mixed time delays , 2007 .

[6]  Marios Mavronicolas,et al.  Efficient Bufferless Packet Switching on Trees and Leveled Networks ∗ , 2005 .

[7]  Shengyuan Xu,et al.  Observer Design for A Class of UncertainState-Delayed Nonlinear Systems , 2006 .

[8]  H. Trinh,et al.  A memoryless state observer for discrete time-delay systems , 1997, IEEE Trans. Autom. Control..

[9]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[11]  Mike Casey,et al.  The Dynamics of Discrete-Time Computation, with Application to Recurrent Neural Networks and Finite State Machine Extraction , 1996, Neural Computation.

[12]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[13]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[14]  R. Kovacevic,et al.  Functional observer and state feedback for input time-delay systems , 1997 .

[15]  J J Torres,et al.  Effects of static and dynamic disorder on the performance of neural automata. , 2005, Biophysical chemistry.

[16]  Daniel W. C. Ho,et al.  State estimation for delayed neural networks , 2005, IEEE Transactions on Neural Networks.

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

[18]  F. Salam,et al.  Adaptive neural observer with forward co-state propagation , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[19]  Shengyuan Xu,et al.  Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay , 2001, Syst. Control. Lett..

[20]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[21]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[22]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

[23]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[24]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..

[25]  P. Shi,et al.  Stochastic stability and robust control for sampled-data systems with Markovian jump parameters , 2006 .

[26]  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).

[27]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[28]  Shengyuan Xu,et al.  Design of observers for a class of discrete-time uncertain nonlinear systems with time delay , 2004, J. Frankl. Inst..

[29]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[30]  P. Balasubramaniam,et al.  State estimation for Markovian jumping recurrent neural networks with interval time-varying delays , 2010 .

[31]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[32]  Zidong Wang,et al.  H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays , 2009, Autom..

[33]  C. Ahn.  Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks , 2010 .