Sampled-data control for mean-square exponential stabilization of memristive neural networks under deception attacks

This paper is concerned with the mean-square exponential stabilization issue of memristive neural networks (MNNs) subject to deception attacks via sampled-data control. The reasons for considering this problem are as follows: (1) Under deception attacks, the state information transmitted in the communication network will be tampered by attackers, which may have an unpredictable impact on the system performance. Moreover, owing to the switching features of MNNs, this makes stability analysis more difficult. (2) In the existing work, it still leave room for improving the security level and the sampling interval. For these reasons, the concept of the security level that measures the anti-attack capability of MNNs is presented for the first time. A secure sampled-data controller is proposed and two looped functions are designed according to the characteristics of deception attacks to improve the security level and the sampling interval. The positivity and symmetry of relevant matrices in the Lyapunov function can be dropped compared to the traditional looped Lyapunov function, which can reduce the conservatism of the result. By utilizing inequality techniques and discrete-time Lyapunov theorem, some sufficient conditions are derived to ensure mean-square exponential stabilization of MNNs in the presence of deception attacks. Lastly, an example of a 3-D MNNs is given to verify the validity of the proposed results. Two superiorities, i.e., improving the security level and enlarging the sampling interval, of the proposed looped functions are also well discussed by a numerical example.