Sampled-data synchronization for fuzzy inertial cellular neural networks and its application in secure communication.

This paper designs the sampled-data control (SDC) scheme to delve into the synchronization problem of fuzzy inertial cellular neural networks (FICNNs). Technically, the rate at which the information or activation of cellular neuronal transmission made can be described in a first-order differential model, but the network response concerning the received information may be dependent on time that can be modeled as a second-order (inertial) cellular neural network (ICNN) model. Generally, a fuzzy cellular neural network (FCNN) is a combination of fuzzy logic and a cellular neural network. Fuzzy logic models are composed of input and output templates which are in the form of a sum of product operations that help to evaluate the information transmission on a rule-basis. Hence, this study proposes a user-controlled FICNNs model with the same dynamic properties as FICNN model. In this regard, the synchronization approach is considerably effective in ensuring the dynamical properties of the drive (without control input) and response (with external control input). Theoretically, the synchronization between the drive-response can be ensured by analyzing the error model derived from the drive-response but due to nonlinearities, the Lyapunov stability theory can be utilized to derive sufficient stability conditions in terms of linear matrix inequalities (LMIs) that will guarantee the convergence of the error model onto the origin. Distinct from the existing stability conditions, this paper derives the stability conditions by involving the delay information in the form of a quadratic function with lower and upper bounds, which are evaluated through the negative determination lemma (NDL). Besides, numerical simulations that support the validation of proposed theoretical frameworks are discussed. As a direct application, the FICNN model is considered as a cryptosystem in image encryption and decryption algorithm, and the corresponding outcomes are illustrated along with security measures.