Stability analysis of hybrid stochastic delayed Cohen-Grossberg neural networks with Levy noise and Markov switching

Authors：Yu, Peilin; Deng, Feiqi^*; Cheng, Pei

Source：JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2022, 359(18): 10831-10848.

DOI：10.1016/j.jfranklin.2022.05.025

• SURE EXPONENTIAL STABILITY
• TIME-VARYING DELAYS
• DIFFERENTIAL-EQUATIONS
• STABILIZATION
• SYNCHRONIZATION

The almost sure exponential stability for hybrid stochastic delayed Cohen-Grossberg neural networks with Levy noise and Markov switching (SDCGNNs-LN-MS) is investigated in the article. Taking full advantage of stationary distribution and by constructing a special Lyapunov function, we get the almost sure exponential stability standard via linear matrix inequality (LMI) for nominal hybrid stochastic system (HSS) without imposing system stability condition. Based on this, we explore the almost sure exponential stability for underlying SDCGNNs-LN-MS according to the comparison principle for sufficiently small time delay tau and an implicit lower bound for t is provided. Finally, the validity of results is demonstrated by an example.