$H_{\infty}$ Controller Design for Networked Systems With Two-Channel Packet Dropouts and FDI Attacks

In this article, the stochastic analysis and $H_{\infty}$ controller design problems of networked systems with packet dropouts and false data injection attacks are investigated. Different from the existing literature, we focus on the linear networked systems with external disturbances and both sensor–controller channel and controller–actuator channel are studied. First, we present a discrete-time modeling framework that leads to a stochastic closed-loop system with randomly varying parameters. To facilitate the analysis and $H_{\infty}$ control of resulting discrete-time stochastic closed-loop system, an equivalent yet analyzable stochastic augmented model is further constructed by matrix exponential computation. Based on this model, a stability condition is derived in the form of linear matrix inequality (LMI) with the aid of a reduced-order confluent Vandermonde matrix, Kronecker product operation, and law of total expectation. Specifically, the dimension of the LMI obtained in this article does not increase as the upper bound of consecutive packet dropouts does, which is also different from the existing literature. Subsequently, a desired $H_{\infty}$ controller is obtained such that the original discrete-time stochastic closed-loop system is exponentially mean-square stable with a prescribed $H_{\infty}$ performance. Finally, a numerical example and a direct current motor system are exploited to substantiate the effectiveness and practicability of the designed strategy.