Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach.

*(English)*Zbl 1322.93079Summary: This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of \(\int^t_{t-h}(h-t-s)^{j\dot x^T}(s)R_j\dot x(s)ds\) \((j=1,2,3)\). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.

##### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

##### Keywords:

generalized neural networks; global asymptotic stability; interval time-varying delay; integral inequality; matrix-based quadratic convex approach
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\textit{X.-M. Zhang} and \textit{Q.-L. Han}, Neural Netw. 54, 57--69 (2014; Zbl 1322.93079)

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