Fuzzy Stabilization of Networked Nonlinear Systems With Multiple Stochastic Transmission Intervals, Packet Losses, and FDI Attacks

Abstract

Networked control systems (NCSs) suffer from various communication imperfections, including varying transmission intervals, packet losses, and false data injection (FDI) attacks. The majority of the existing literature on NCSs tends to emphasize certain aspects while neglecting others. In this article, we propose a general framework for addressing the stabilization problem of networked nonlinear systems that incorporates multiple stochastic transmission intervals (MSTIs), successive packet losses (SPLs), and FDI attacks. We assume that the nonlinear system can be precisely modeled using a Takagi–Sugeno (T–S) fuzzy system. MSTIs can be described using the categorical distribution, while both the sensor-to-controller channel and the controller-to-actuator channel are affected by SPLs and FDI attacks. In order to facilitate the stabilization problem, we first establish the equivalent stochastic transmission interval between adjacent nonpacket-loss instants, where the occurrence probability of the length of the equivalent transmission interval can be accurately calculated by using the probabilistic information of SPLs and MSTIs. Furthermore, considering two-channel FDI attacks, a discrete-time T–S fuzzy system model is obtained. The controller design conditions, represented by linear matrix inequalities (LMIs), are derived based on this model. Specifically, using a novel matrix reconstruction approach, the dimension of the obtained controller design condition does not change with the number of maximum packet losses and the number of MSTIs, which is more general than existing results and avoids the high computational complexity associated with solving LMIs in some cases. Finally, the effectiveness of the proposed method is demonstrated through a numerical example.