Secure Control Strategies for Stochastically Sampled Systems Against DoS/Deception Attacks: A General Design Algorithm

In this paper, secure control strategies are developed for stochastically sampled systems under Denial-of-Service (DoS)/deception attacks. The actual sampling intervals deviate from their nominal values, and these sampling inaccuracies are modeled as uniformly bounded random variables following a truncated Gaussian distribution. Unlike existing studies on sampled-data systems affected by attack-induced packet losses, the obtained stability condition can be directly utilized regardless of variations in the maximum number of consecutive DoS attacks. We begin by developing a continuous-time modeling framework that enables stabilization analysis for the stochastically sampled systems exposed to DoS and deception attacks. To ensure stochastic stability and facilitate secure control, a discrete-time reformulation of the continuous-time model is then introduced. It is shown that the continuous-time system is stochastically stable if and only if its discrete-time counterpart maintains stochastic stability. Following this, a stability condition is derived and a controller synthesis algorithm is proposed to guarantee the stochastic stability of the continuous-time stochastically sampled systems subject to DoS/deception attacks. Finally, simulation results are presented to demonstrate the efficacy of the proposed controller algorithm.