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A decent vehicle-to-grid (V2G) control scheme improves voltage stability and grid reliability of distribution networks (DNs) by providing reactive power and ancillary services. However, unknown malicious attacks in cyber layers and uncertain EV charging/unplugging in physical layers will disturb the measurement process, leading to controller parameters’ mismatching and severe voltage violations. This paper proposes a robust V2G voltage control scheme for DNs investigating cyber attacks and EV customer interruptions. Firstly, the impact of cyber attacks is characterized by time-varying uncertain matrices function with Lebesgur measurable elements, while the EV customer interruptions are represented by Signum variables. Then, a new state-space equation for V2G voltage control in DNs is constructed by incorporating above matrices function and Signum variables. Moreover, a robust voltage controller is proposed for measurement disordered V2G systems to suppress voltage violations while achieving $H_{\infty }$ performance. By utilizing linear matrix inequality (LMI) techniques, sufficient conditions for system closed-loop exponentially mean-square stability and the controller parameter tuning are presented. Case studies conducted on modified IEEE European low voltage test feeder compare two voltage deviation indices of the proposed controller with those of existing methods, verifying the effectiveness of the proposed approach against measurement anomalies.