Stochastic stability analysis of networked control systems with random cryptographic protection under random zero-measurement attacks

Security issues in networked control systems (NCSs) have received increasing attention in recent years. However, security protection often requires extra energy consumption, computational overhead, and time delays, which could adversely affect the real-time and energy-limited system. In this paper, random cryptographic protection is implemented. It is less expensive with respect to computational overhead, time, and energy consumption, compared with persistent cryptographic protection. Under the consideration of weak attackers who have little system knowledge, ungenerous attacking capability and the desire for stealthiness and random zero-measurement attacks are introduced as the malicious modification of measurements into zero signals. NCS is modeled as a stochastic system with two correlated Bernoulli distributed stochastic variables for implementation of random cryptographic protection and occurrence of random zero-measurement attacks; the stochastic stability can be analyzed using a linear matrix inequality (LMI) approach. The proposed stochastic stability analysis can help determine the proper probability of running random cryptographic protection against random zero-measurement attacks with a certain probability. Finally, a simulation example is presented based on a vertical take-off and landing (VTOL) system. The results show the effectiveness, robustness, and application of the proposed method, and are helpful in choosing the proper protection mechanism taking into account the time delay and in determining the system sampling period to increase the resistance against such attacks.