Switched Event-Triggered $\mathcal {H}_{\infty }$ Security Control for Networked Systems Vulnerable to Aperiodic DoS Attacks

Abstract

This paper investigates switched event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> security control for networked systems vulnerable to aperiodic denial-of-service (ADoS) attacks. An anti-attack switched event-triggered mechanism (ATASETM) is designed by considering the impact of ADoS attacks on the systems. Based on the mechanism, the entire time interval is split into rest intervals, continuous detection intervals, residual intervals, and ADoS active-attack intervals. The closed-loop system (CLS) is represented as a three-mode switched system by merging these intervals. Subsequently, a three-piecewise Lyapunov function is constructed for fewer conservative criteria to ensure that the CLS is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> exponentially stable. An exact expression of the relationship between the decay rate and length of the dormant- and active-attack intervals is obtained. On the basis of the proposed criteria, a joint-design strategy is developed in terms of linear matrix inequalities for the desired trigger matrix and feedback gain. Lastly, a satellite control system and an inverted pendulum model are used to validate the ATASETM-based stability analysis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> security control approaches. Numerical results demonstrate that the maximum allowable exponential decay rate decreases with increasing attack time (and vice versa), and the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> performance level becomes worse as the attack time or the difficulty of the event triggering increases.