Non-Weighted L2-Gain Analysis for Synchronization of Switched Nonlinear Time-Delay Systems With Random Injection Attacks

The current paper is devoted to studying global asymptotic <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> drive-response synchronization for a kind of switched nonlinear time-delay systems with output random injection attacks (IAs). An attack-decomposition method is proposed to derive an attack-free signal, by which an observer is designed to estimate the state of the driving system. Then, two mode-dependent event-triggering mechanisms (MDETMs) are respectively designed for observer-controller (O-C) and controller-actuator (C-A) channels to save the communication resources as much as possible. In order to analyze the effects of the switching on the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance, a mode-dependent discretized Lyapunov-Krasovskii functional (LKF) is developed, which has the merit of monotone decreasing on any time-interval and switching instants. Sufficient criteria are given to ensure the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> synchronization with non-weighted <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain, whether the attack is related to the output or not. Numerical simulations are provided to verify the non-weighted <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain performance with low conservatism.