Finite-time and fixed-time synchronization of discontinuous complex networks: a unified control framework design. (English) Zbl 1390.93105
Summary: This paper is concerned with the finite-time and fixed-time synchronization of complex networks with discontinuous nodes dynamics. Firstly, under the framework of Filippov solution, a new theorem of finite-time and fixed-time stability is established for nonlinear systems with discontinuous right-hand sides by using mainly reduction to absurdity. Furthermore, for a class of discontinuous complex networks, a general control law is firstly designed. Under the unified control framework and the same conditions, the considered networks are ensured to achieve finite-time or fixed-time synchronization by only adjusting the value of a key control parameter. Based on the similar discussion, a unified control strategy is also provided to realize respectively asymptotical, exponential and finite-time synchronization of the addressed networks. Finally, the derived theoretical results are supported by an example with numerical simulations.
MSC:
| 93A15 | Large-scale systems |
| 93A14 | Decentralized systems |
| 93C10 | Nonlinear systems in control theory |
| 93D99 | Stability of control systems |
Keywords:
finite-time and fixed-time synchronization; complex networks; discontinuous nodes dynamics; Filippov solution; finite-time and fixed-time stability; nonlinear systems with discontinuous right-hand sidesReferences:
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