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**Distributed containment control of networked fractional-order systems with delay-dependent communications.**
*(English)*
Zbl 1251.93096

Summary: We are concerned with a containment problem of networked fractional-order system with multiple leaders under a fixed directed interaction graph. Based on the neighbor rule, a distributed protocol is proposed in delayed communication channels. By employing the algebraic graph theory, matrix theory, Nyquist stability theorem, and frequency domain method, it is analytically proved that the whole follower agents will flock to the convex hull which is formed by the leaders. Furthermore, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is obtained. As a special case, the interconnection topology under the undirected case is also discussed. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

34A08 | Fractional ordinary differential equations |

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\textit{X. Liu} et al., J. Appl. Math. 2012, Article ID 840873, 13 p. (2012; Zbl 1251.93096)

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