Robust stability of discrete-time LPD neural networks with time-varying delay.

*(English)*Zbl 1221.93216Summary: 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 |

##### Keywords:

neural network; robust stability; polytopic type uncertainties; linear matrix inequality (LMI); linear parameter dependent (LPD); Lyapunov function; S-procedure##### Software:

LMI toolbox
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\textit{S. Udpin} and \textit{P. Niamsup}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 11, 3914--3924 (2009; Zbl 1221.93216)

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##### References:

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