Asymptotic and finite-time cluster synchronization of neural networks via two different controllers. (English) Zbl 1500.93118
Summary: In this paper, by using a pinning impulse controller and a hybrid controller respectively, the research difficulties of asymptotic synchronization and finite time cluster synchronization of time-varying delayed neural networks are studied. On the ground of Lyapunov stability theorem and Lyapunov-Razumikhin method, a novel sufficient criterion on asymptotic cluster synchronization of time-varying delayed neural networks is obtained. Utilizing finite-time stability theorem and hybrid control technology, a sufficient criterion on finite-time cluster synchronization is also obtained. In order to deal with time-varying delay and save control cost, pinning pulse control is introduced to promote the realization of asymptotic cluster synchronization. Following the idea of pinning control scheme, we design a progressive hybrid control to promote the realization of finite time cluster synchronization. Finally, an example is given to illustrate the theoretical results.
MSC:
| 93D40 | Finite-time stability |
| 93D20 | Asymptotic stability in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C27 | Impulsive control/observation systems |
Keywords:
Lyapunov-Razumikhin method; time-varying delay; finite-time cluster synchronization; pinning impulsive control; hybrid controlReferences:
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