State estimation for the two-time-scale CPSs: Handling asynchronous multimodal attacks

Abstract

This paper studies the state estimation issue for two-time-scale cyber–physical systems (TTSCPSs) with slow and fast transmission channels (TCs) under asynchronous cyber attacks. A novel multimodal attack model is established, by which the attack is generated with alternating modes of denial-of-service and deception attacks in each TC. To mitigate the detrimental effects of such attacks, a unique $\varepsilon$-dependent estimator and corresponding gain scheduling rule are designed. Then, by constructing an $\varepsilon$-dependent Lyapunov function, sufficient conditions are derived to ensure that the estimation error system is exponentially mean square stable with a prescribed $H_{\infty }$ performance. It is worth mentioning that the possible numerical stiffness caused by two-time-scale properties is averted in the designed estimation algorithm. Finally, the effectiveness of the developed algorithm is illustrated by two simulation examples.