Exponential Generalized $$H_2$$H2 Filtering of Delayed Static Neural Networks

This paper is concerned with the problem of generalized $$H_2$$H2 filter design for static neural networks with time-varying delay. A double-integral inequality and the reciprocally convex combination technique are employed to handle the cross terms appeared in the time-derivative of the Lyapunov functional. An improved delay-dependent design criterion is presented by means of linear matrix inequalities. It is shown that the gain matrix of the desired filter and the optimal performance index are simultaneously achieved by solving a convex optimization problem. Moreover, the upper bound of the exponential decay rate of the filtering error system can be also easily obtained. An example with simulation is exploited to illustrate the effectiveness of the developed result.

[1]  Hong Qiao,et al.  A comparative study of two modeling approaches in neural networks , 2004, Neural Networks.

[2]  Dan Zhang,et al.  Estimator Design for Discrete-Time Switched Neural Networks With Asynchronous Switching and Time-Varying Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Zhigang Zeng,et al.  Global Stability of a General Class of Discrete-Time Recurrent Neural Networks , 2005, Neural Processing Letters.

[4]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Jinde Cao,et al.  Stability in static delayed neural networks: A nonlinear measure approach , 2006, Neurocomputing.

[6]  Frédéric Gouaisbaut,et al.  Delay-dependent stability analysis of linear systems with time-varying delay , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  Guoping Liu,et al.  Improved delay-range-dependent stability criteria for linear systems with time-varying delays , 2010, Autom..

[8]  Qing-Guo Wang,et al.  Delay-Dependent State Estimation for Delayed Neural Networks , 2006, IEEE Transactions on Neural Networks.

[9]  Z. Zeng,et al.  Global exponential stability in Lagrange sense for recurrent neural networks with time delays , 2008 .

[10]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[11]  Qing Zhu,et al.  Design of exponential state estimator for neural networks with distributed delays , 2009 .

[12]  James Lam,et al.  Stability and Dissipativity Analysis of Static Neural Networks With Time Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[14]  Jinde Cao,et al.  Guaranteed performance state estimation of static neural networks with time-varying delay , 2011, Neurocomputing.

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

[16]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[17]  Hanyong Shao,et al.  Less conservative delay-dependent stability criteria for neural networks with time-varying delays , 2010, Neurocomputing.

[18]  Zidong Wang,et al.  State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays , 2012, Neural Processing Letters.

[19]  Tzuu-Hseng S. Li,et al.  Walking Motion Generation, Synthesis, and Control for Biped Robot by Using PGRL, LPI, and Fuzzy Logic , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[21]  James Lam,et al.  Stability analysis of static recurrent neural networks using delay-partitioning and projection , 2009, Neural Networks.

[22]  Chien-Yu Lu,et al.  Design of Delay-Dependent Exponential Estimator for T–S Fuzzy Neural Networks with Mixed Time-Varying Interval Delays Using Hybrid Taguchi-Genetic Algorithm , 2012, Neural Processing Letters.

[23]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

[24]  Jinde Cao,et al.  State estimation for static neural networks with time-varying delay , 2010, Neural Networks.

[25]  A. F. Murray,et al.  Fault tolerance via weight noise in analog VLSI implementations of MLPs-a case study with EPSILON , 1998 .

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

[27]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[28]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  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.

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

[31]  Qing-Long Han,et al.  Robust H infinity filtering for a class of uncertain linear systems with time-varying delay. , 2008 .

[32]  Gang Feng,et al.  Delay-Dependent $H_{\infty}$ and Generalized $H_{2}$ Filtering for Delayed Neural Networks , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.