\(\mathrm{L}_{\mathrm{p}}\) stability analysis of neural networks with multiple time-varying delays. (English) Zbl 1521.93132
Summary: This paper studies the problem of \(\mathrm{L}_{\mathrm{p}}\) stability analysis of neural networks (NNs) with multiple time-varying delays. The delays can be bounded or unbounded. Firstly, a new method based on system solutions is proposed, from which new \(\mathrm{L}_{\mathrm{p}}\) stability criteria are obtained. On the one hand, the method is convenient to deal with the cases of multiple delays. On the other hand, this method does not need to establish any Lyapunov-Krasovskii functional (LKF), which can greatly reduce the amount of calculations. The obtained \(\mathrm{L}_{\mathrm{p}}\) stability conditions are simpler, and can be checked by standard software tools. The advantages of the obtained \(\mathrm{L}_{\mathrm{p}}\) stability conditions are demonstrated with representative numerical examples. It is worth emphasizing that this article is the first time to analyze the \(\mathrm{L}_{\mathrm{p}}\) stability of NNs with multiple time-varying delays.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B70 | Networked control |
| 93C43 | Delay control/observation systems |
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