Input-to-state practical stability of switched systems with unstabilizable modes under deception attacks

In this paper, the input-to-state practical stability (ISpS) of switched systems with unstabilizable modes is addressed against the impact of deception attacks and external disturbances. Unlike conventional approaches that solely consider stabilizable modes, the switched systems with unstabilizable modes are investigated and the constraints on unstabilizable modes are relaxed from fixed constant to the reciprocal of the average time over varying periods. Due to the sampling scheme and deception attacks, the asynchronous issue between controller mode and subsystem mode gives rise to a significant increase in system complexity, particularly in regard to dynamics. Furthermore, an adaptive controller incorporating a corrective signal is devised to counteract the effects of deception attacks and a mode-dependent average dwell time (MDADT)-based switching signal is formulated to stabilize the proposed systems. A sufficient criterion is put forward to ensure the ISpS with a desired security level of the system under deception attacks, moreover, the conclusion clarifies the relationship between the average time ratio of unstabilizable modes and the synchronous as well as asynchronous durations of the system when exposed to a deception attack. The effectiveness of the proposed methodology is validated through a numerical example and an application booster converter example.