## Abstract

This paper investigates \({H_\infty }\)/passive synchronization for a class of complex dynamical networks with semi-Markovian jump and coupling time-varying delays based on sampled-data control. The main purpose is to design a sampled-data controller, using discrete controller approach, to ensure \({H_\infty }\)/passive synchronization of the closed-loop error system. By constructing a novel Lyapunov–Krasovskii functional, in which the characteristics of the sampled-data are fully considered, then combining some integral inequalities, free weighting matrices and convex combination method, we establish the \({H_\infty }\)/passive synchronization criterion for a class of complex dynamical networks with semi-Markovian jump. Moreover, the proposed synchronization criterion can be simplified into the form of linear matrix inequalities using Matlab toolbox. Finally, two numerical examples are given to verify the validity and practicability of the theoretical results.

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This work is supported by National Natural Science Foundation of China (No. 61273004) and the Natural Science Foundation of Hebei province (No. F2018203099).

Communicated by Luz de Teresa.

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Li, J., Ma, Y. & Fu, L. \({H_\infty }\)/passive synchronization for complex dynamical networks with semi-Markovian jump and coupling time-varying delays based on sampled-data control.
*Comp. Appl. Math.* **39, **73 (2020). https://doi.org/10.1007/s40314-020-1087-y

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### Keywords

- \({H_\infty }\)/passive synchronization
- Complex dynamical networks
- Semi-Markovian jump
- Coupling time-varying delays
- Sampled-data

### Mathematics Subject Classification

- 93C42
- 93C73