An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays.

*(English)*Zbl 1157.93039Summary: This paper deals with the problem of global exponential stability for a general class of stochastic high-order neural networks with mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both mixed time delays and Markovian switching. By employing a new Lyapunov-Krasovskii functional and conducting stochastic analysis, a Linear Matrix Inequality (LMI) approach is developed to derive the criteria ensuring exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, and hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

##### MSC:

93E15 | Stochastic stability in control theory |

60J75 | Jump processes (MSC2010) |

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

##### Keywords:

high-order neural networks; stochastic neural networks; delay-dependent criteria; Markovian switching; global exponential stability; linear matrix inequality
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\textit{Y. Liu} et al., Nonlinear Anal., Hybrid Syst. 2, No. 1, 110--120 (2008; Zbl 1157.93039)

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