Output synchronization of fractional-order multi-layer network via quantized pinning control under stochastic cyber attacks

In practical applications, loads of single complex network models cannot meet the research requirements owing to the interaction between network layers. Furthermore, the measurability of state information is rather difficult in the light of some uncontrollable factors. In view of these facts, we are mainly devoted to researching the output synchronization problem of fractional-order multi-layer network with output coupling under stochastic deceptive attacks. By utilizing the Lyapunov function, graph theoretic, and LMI techniques, some sufficient criteria are introduced to achieve output synchronization. Firstly, a quantized pinning scheme is designed to discuss the output synchronization of fractional-order multi-layer networks in the absence of cyber attacks. Subsequently, in view of the fact that fractional-order multi-layer networks are susceptible to malicious attacks of stochastic networks in synchronization process, an adaptive quantized pinning control strategy is developed. This strategy can adjust its personal parameters according to the state changes of nodes. Especially, the output matrix is no more restricted to a diagonal matrix, and the relationship between the output matrix and output synchronization is further acquired, which increases the applicability of controlled system. Ultimately, two persuasive numerical examples are used to expound the availability and superiority of theoretical results.