Abstract
In this paper, by using some analytic techniques, several sufficient conditions are given to ensure the passivity of a general form of recurrent neural network with multiple delays. The passivity conditions are presented in terms of a negative semi-definite matrix declared. They are easily verifiable and easier to check computing with some conditions in terms of complicated linear matrix inequality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circ. Syst. 42, 354–366 (1995)
Zeng, Z.G., Wang, J.: Analysis and Design of Associative Memories Based on Recurrent Neural Networks with Linear Saturation Activation Functions and Time-varying Delays. Neural Computation 19, 2149–2182 (2007)
Liao, X.X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits and Systems 50, 268–275 (2003)
Yi, Z., Heng, A., Leung, K.S.: Convergence Analysis of Cellular Neural Networks with Unbounded Delay. IEEE Trans. Circuits Syst. 48, 680–687 (2001)
Chen, T.P., Rong, L.B.: Robust Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-Delays. IEEE Transactions on Neural Networks 15, 203–206 (2004)
Liao, X.F., Li, C.G., Wong, K.W.: Criteria for Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 17, 1401–1414 (2004)
Cao, J.: Results Concerning Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks. Physics Letters 307, 136–147 (2003)
Zeng, Z.G., Wang, J., Liao, X.X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Trans. Circuits and Systems Part 50, 1353–1358 (2003)
Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Syst. 51, 2313–2324 (2004)
Zeng, Z.G., Wang, J.: Improved Conditions for Global Exponential Stability of Recurrent Neural Network with Time-varying Delays. IEEE Trans on Neural Networks 17, 623–635 (2006)
Zeng, Z.G., Wang, J.: Global Exponential Stability of Recurrent Neural Networks with Time-varying Delays in the Presence of Strong External Stimuli. Neural Networks 19, 1528–1537 (2006)
Zeng, Z.G., Wang, J.: Multiperiodicity of Discrete-time Delayed Neural Networks Evoked by Periodic External Inputs. IEEE Transactions on Neural Networks 17, 1141–1151 (2004)
Zeng, Z.G., Wang, J.: Complete Stability of Cellular Neural Networks with Time-varying Delays. IEEE Transactions on Circuits and Systems 53, 944–955 (2006)
Byrnes, C.I., Isidori, A., Willems, J.C.: Passivity, Feedback Equivalence, and the Global Stabilization of Minimum Phase Nonlinear Systems. IEEE Transactions on Automatic Control 36, 1228–1240 (1991)
Lozano, R., Brogliato, B., Egeland, O., Maschke, B.: Dissipative Systems Analysis and Control: Theory and Applications. Springer, London (2000)
Commuri, S., Lewis, F.L.: CMAC Neural Networks for Control of Nonlinear Dynamical Systems: Structure, Stability, and Passivity. Automatica 33, 635–641 (1997)
Yu, W., Li, X.: New Results on System Identification with Dynamic Neural Networks. IEEE Trans. Neural Networks 12, 412–417 (2001)
Yu, W.: Passivity Analysis for Dynamic Multilayer Neuro Identifier. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50, 173–178 (2003)
Li, C., Liao, X.: Passivity Analysis of Neural Networks with Time Delays. IEEE Trans. Circuits Syst. II, Exp. Briefs 52, 471–475 (2005)
Lou, X., Cui, B.: Passivity Analysis of Integro-differential Neural Networks with Time-varying Delays. Neurocomputing 70, 1071–1078 (2007)
Park, J.H.: Further Results on Passivity Analysis of Delayed Cellular Neural Networks. Chaos, Solitons and Fractals 34, 1546–1551 (2007)
Liao, X.X., Wang, J.: Global Dissipativity of Continuous-Time Recurrent Neural Networks with Time Delay. Phys. Rev. 68, 1–7 (2003)
Song, Q., Zhao, Z.: Global Dissipativity of Neural Networks with both Variable and Unbounded Delays. Chaos, Solitons and Fractals 25, 393–401 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Huang, J., Liu, J. (2009). Passivity Analysis of a General Form of Recurrent Neural Network with Multiple Delays. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01513-7_86
Download citation
DOI: https://doi.org/10.1007/978-3-642-01513-7_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01512-0
Online ISBN: 978-3-642-01513-7
eBook Packages: Computer ScienceComputer Science (R0)