Security control for two-time-scale cyber physical systems with multiple transmission channels under DoS attacks: The input-to-state stability

Abstract This paper investigates the security control problem for a class of two-time-scale cyber-physical systems (TTSCPSs) with multiple transmission channels under the denial-of-service (DoS) attacks. A linear TTSCPSs model is first proposed with slow and fast transmission channels, which correspond to slow and fast physical components in terms of their communicating capacities and sampling rates. The measurement data-packets are transmitted via slow and fast transmission channels which are compromised by asynchronous DoS attacks. A novel composite controller depending on the singular perturbation parameter (SPP) is formulated and corresponding switching laws are designed to achieve certain resilience against DoS attacks. Then, by establishing a SPP-dependent Lyapunov function, sufficient conditions are obtained on the duration and frequency of the DoS attacks, such that, for any SPP less than or equal to a predefined upper bound, the input-to-state stability can be guaranteed for the closed-loop TTSCPSs. Finally, a networked DC motor control system is employed to demonstrate the effectiveness of the proposed security control algorithm.