##
**New robust exponential stability results for discrete-time switched fuzzy neural networks with time delays.**
*(English)*
Zbl 1268.93118

Summary: We provide a novel result on robust exponential stability for a class of uncertain discrete-time switched fuzzy neural networks (DSFNNs) with time-varying delays and parameter uncertainties. By implementing an average dwell time approach with a new Lyapunov-Krasovskii functional, we obtain some delay-dependent sufficient conditions guaranteeing the robust exponential stability of the considered switched fuzzy neural networks. In other words, a class of switching signals specified by the average dwell time is identified to guarantee the exponential stability of the considered DSFNNs. The obtained conditions are formulated in terms of Linear Matrix Inequalities (LMIs) which can be easily verified via the LMI toolbox. Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained results.

### Keywords:

switched neural networks; fuzzy neural networks; robust exponential stability; average Dwell time; linear matrix inequality### Software:

LMI toolbox
PDF
BibTeX
XML
Cite

\textit{K. Mathiyalagan} et al., Comput. Math. Appl. 64, No. 9, 2926--2938 (2012; Zbl 1268.93118)

Full Text:
DOI

### References:

[1] | Morse, A.S., Supervisory control of families of linear set-point controllers, part I: exact matching, IEEE transactions on automatic control, 41, 1413-1431, (1996) · Zbl 0872.93009 |

[2] | Cai, C., Dwell-time approach to input output stability properties for a class of discrete-time dynamical systems, Systems & control letters, 60, 383-389, (2011) · Zbl 1225.93070 |

[3] | Sun, X.; Zhao, J.; Hill, D.J., Stability and \(L_2\)-gain analysis for switched delay systems: a delay-dependent method, Automatica, 42, 1769-1774, (2006) · Zbl 1114.93086 |

[4] | Zhang, W.; Yu, L., Stability analysis for discrete-time switched time-delay systems, Automatica, 45, 2265-2271, (2009) · Zbl 1179.93145 |

[5] | Kwon, O.M.; Park, J.H., New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays, Applied mathematics and computations, 205, 417-427, (2008) · Zbl 1162.34060 |

[6] | Kwon, O.M.; Park, J.H., Improved delay-dependent stability criterion for neural networks with time-varying delays, Physics letters A, 373, 529-535, (2009) · Zbl 1227.34030 |

[7] | Kwon, O.M.; Park, J.H.; Lee, S.M., On robust stability for uncertain cellular neural networks with interval time-varying delays, IET control theory and applications, 2, 625-634, (2008) |

[8] | Kwon, O.M.; Lee, S.M.; Park, J.H., Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays, Physics letters A, 374, 1232-1241, (2010) · Zbl 1236.92006 |

[9] | Kwon, O.M.; Lee, S.M.; Park, J.H., Improved results on stability analysis of neural networks with time-varying delays: novel delay-dependent criteria, Modern physics letters B, 24, 775-789, (2010) · Zbl 1192.93109 |

[10] | Sakthivel, R.; Raja, R.; Marshal Anthoni, S., Exponential stability for delayed stochastic bidirectional associative memory neural networks with Markovian jumping and impulses, Journal of optimization theory & applications, 150, 166-187, (2011) · Zbl 1226.93134 |

[11] | Sakthivel, R.; Samidurai, R.; Marshal Anthoni, S., New exponential stability criteria for stochastic BAM neural networks with impulses, Physica scripta, 82, (2010), Art no. 045802 · Zbl 1195.82066 |

[12] | Liu, Y.; Wang, Z.; Liu, X., Asymptotic stability for neural networks with mixed time-delays: the discrete-time case, Neural networks, 22, 67-74, (2009) · Zbl 1335.93112 |

[13] | Luo, M.; Zhong, S.; Wang, R.; Kang, W., Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays, Applied mathematics and computation, 209, 305-313, (2009) · Zbl 1157.93027 |

[14] | Song, Q.; Liang, J.; Wang, Z., Passivity analysis of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, 72, 1782-1788, (2009) |

[15] | Song, Q.; Wang, Z., Stability analysis of impulsive stochastic cohen – grossberg neural networks with mixed time delays, Physica A, 387, 3314-3326, (2008) |

[16] | Wu, L.; Feng, Z.; Zheng, W.X., Exponential stability analysis for delayed neural networks with switching parameters: average Dwell time approach, IEEE transactions on neural networks, 21, 1396-1407, (2010) |

[17] | Zhang, D.; Yu, L., Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays, Nonlinear dynamics, (2011) |

[18] | Wu, Z.; Shi, P.; Su, H.; Chu, J., Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay, Neurocomputing, 74, 1626-1631, (2011) |

[19] | Hou, L.; Zong, G.; Wu, Y., Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay, Nonlinear analysis: hybrid systems, 5, 525-534, (2011) · Zbl 1238.93075 |

[20] | Huang, H.; Qu, Y.; Li, H., Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty, Physics letters A, 345, 345-354, (2005) · Zbl 1345.92013 |

[21] | Zhang, Y.; Xu, S.; Zeng, Z., Novel robust stability criteria of discrete-time stochastic recurrent neural networks with time delay, Neurocomputing, 72, 3343-3351, (2009) |

[22] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE transactions on systems, man and cybernetics, 15, 116-132, (1985) · Zbl 0576.93021 |

[23] | Tanaka, K.; Iwasaki, M.; Wang, H.O., Stability and smoothness conditions for switching fuzzy systems, (), 2474-2478 |

[24] | Tanaka, K.; Iwasaki, M.; Wang, H.O., Stable switching fuzzy control and its application to a hovercraft type vehicle, (), 804-809 |

[25] | Balasubramaniam, P.; Syed Ali, M., Stability analysis of takagi – sugeno stochastic fuzzy Hopfield neural networks with discrete and distributed time varying delays, Neurocomputing, 74, 1520-1526, (2011) · Zbl 1211.37101 |

[26] | Balasubramaniam, P.; Chandran, R., Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay, Communications in nonlinear science and numerical simulation, 16, 2098-2108, (2011) · Zbl 1221.34214 |

[27] | Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S., New stability and stabilization criteria for fuzzy neural networks with various activation functions, Physica scripta, 84, (2011), Art no. 015007 · Zbl 1219.82131 |

[28] | Syed Ali, M.; Balasubramaniam, P., Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays, Chaos, solitons and fractals, 42, 2191-2199, (2009) · Zbl 1198.93192 |

[29] | Syed Ali, M.; Balasubramaniam, P., Exponential stability of uncertain stochastic fuzzy BAM neural networks with time-varying delays, Neurocomputing, 72, 1347-1354, (2009) · Zbl 1198.93192 |

[30] | Song, Q.; Cao, J., Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses, Journal of the franklin institute, 345, 39-59, (2008) · Zbl 1167.93369 |

[31] | Tang, Y.; Fang, J.; Xia, Min; Gu, X., Synchronization of Takagi sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays, Applied mathematical modelling, 34, 843-855, (2010) · Zbl 1185.93145 |

[32] | Sakthivel, R.; Mathiyalagan, K.; Marshal Anthoni, S., Design of a passification controller for uncertain fuzzy Hopfield neural networks with time-varying delays, Physica scripta, 84, (2011), Art no. 045024 · Zbl 1263.34117 |

[33] | Tanaka, K.; Iwasaki, M.; Wang, H.O., Switching control of an R/C hovercraft: stabilization and smooth switching, IEEE transactions on systems, man and cybernetics, 31, 853-863, (2001) |

[34] | Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 135-156, (1992) · Zbl 0758.93042 |

[35] | Savkin, A.V.; Matveev, A.S., Cyclic linear differential automata: a simple class of hybrid dynamical systems, Automatica, 36, 727-734, (2000) · Zbl 0986.93043 |

[36] | Choi, D.J.; Park, P.G., Guaranteed cost controller design for discrete-time switching fuzzy systems, IEEE transactions on systems, man, and cybernetics, 34, 110-119, (2004) |

[37] | Dong, J.; Yang, G.H., Dynamic output feedback control synthesis for continuous-time TS fuzzy systems via a switched fuzzy control scheme, IEEE transactions on systems, man, and cybernetics, 38, 1166-1175, (2008) |

[38] | Dong, J.; Yang, G.H., \(H_\infty\) controller synthesis via switched PDC scheme for discrete-time TS fuzzy systems, IEEE transactions on fuzzy systems, 17, 544-555, (2009) |

[39] | Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural networks, 19, 667-675, (2006) · Zbl 1102.68569 |

[40] | Boyd, B.; Ghoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.