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Robust stability of discrete-time LPD neural networks with time-varying delay. (English) Zbl 1221.93216
Summary: This paper presents a new approach to the robust stability of discrete-time LPD neural networks with time-varying delay and with normed bounded uncertainties as well as polytopic type uncertainties. Based on Lyapunov stability theory and the S-procedure, we derive robust stability criteria in terms of linear matrix inequalities (LMI) which are solvable by several available algorithms. We show that some of the existing results on robust stability of neural networks are corollaries of main results of this paper. Numerical examples are given to illustrate the effectiveness of our theoretical results.

##### MSC:
 93D09 Robust stability 34K20 Stability theory of functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics
LMI toolbox
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##### References:
 [1] Bengea S, DeCarlo R, Corless M, Rizzoni G. A polytopic system approach for the hybrid control of a diesel engine using VGT/EGR, ECE technical reports, Purdue University, IM; 2002. p. 1-61. [2] Botto, M.A.; Wams, B.; Boom, T.; Costa, J., Robust stability of feedback linearised systems modelled with neural networks: dealing with uncertainty, Eng appl artif intell, 13, 659-670, (2000) [3] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia (PA) · Zbl 0816.93004 [4] Cauët, S.; Rambault, L.; Bachelier, O.; Mehdi, D., Parameter-dependent Lyapunov functions applied to analysis of induction motor stability, Contr eng pract, 10, 337-345, (2002) [5] Chua, L.O.; Yang, L., Cellular neural networks: theory, IEEE trans circ syst, 35, 1257-1272, (1998) · Zbl 0663.94022 [6] Gahinet, P.; Nemirovsky, A.; Laub, A.J.; Chilali, M., LMI control toolbox: for use with Matlab, (1995), The MATH Works, Inc. [7] Gao, H.; Lam, J.; Wang, C., Mixed $$H_2 / H_\infty$$ filtering for continuous-time polytopic systems: a parameter-dependent approach, Circ syst signal process, 24, 689-702, (2005) · Zbl 1102.94033 [8] He, Y.; Wang, Q.G.; Wu, M., LMI-based stability criteria for neural networks with multiple time-varying delays, Physica D, 212, 126-136, (2005) · Zbl 1097.34054 [9] He, Y.; Wang, Q.G.; Zang, W.X., Global robust stability for delayed neural networks with polytopic type uncertainty, Chaos solitons fractals, 26, 1349-1354, (2005) · Zbl 1083.34535 [10] Khalil, H.K., Nonlinear system, (1986), McMillan Publishing Company NewYork [11] Liu, Y.; Wang, Z.; Serrano, A.; Liu, X., Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis, Phys lett A, 362, 480-488, (2007) [12] Liu, Y.; Wang, Z.; Liu, X., Robust stability of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, 71, 823-833, (2008) [13] Phat, V.N., Robust stability and stabilizability of uncertain linear hybrid systems with state delays, IEEE trans circ syst, 52, 94-98, (2005) [14] Roska, T.; Chua, L.O., Cellular neural networks with nonlinear and delay-type template, Int J circ theor appl, 20, 469-481, (1992) · Zbl 0775.92011 [15] Singh, V., New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties, Chaos solitons fractals, 30, 1165-1171, (2005) · Zbl 1142.34353 [16] Zhang, H.; Liao, X., LMI-base robust stability analysis of neural networks with time-varying delay, Neurocomputing, 67, 306-312, (2005)
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