Complex Systems and Networks by Jinhu Lü Xinghuo Yu Guanrong Chen & Wenwu Yu

Author:Jinhu Lü, Xinghuo Yu, Guanrong Chen & Wenwu Yu
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

9.3.3 Numerical Simulation

In this section, some examples are given to verify the effectiveness of the theoretical analysis.

Fig. 9.5The communication topology

Example 9.1

Assume that the communication topology is shown in Fig. 9.5, where node 0 is the leader while nodes 1, 2, 3, and 4 are the followers. The corresponding Laplacian matrix is

and the leader adjacency matrix is

Some calculations give that the eigenvalues of are 0.3820, 2.6180, and .

Choose , then the . By using Theorem 9.3, the leader-following consensus can be ensured. For the brevity of expression, we use , x, and e to denote , x(t) with , and e(t) with , respectively. Then, one can see that the followers track the leader asymptotically as shown in Figs. 9.6 and 9.7.

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