Sampled-data stabilization for networked control systems under deception attack and the transmission delay

For the stability analysis and stabilization synthesis problems, this paper considers networked control systems (NCSs) with the transmission delay and the deception attack under aperiodic samplings, where the deception attack and its activation function are represented as a sector bound function and a random variable with Bernoulli distribution, respectively. This paper proposes the stability and stabilization criteria for the NCSs by constructing Lyapunov- Krasovskii (L-K) functionals with continuous functionals and looped-functionals. Compared with the literature, the proposed continuous functionals take into account the mixed delay including the transmission delay and the maximum allowable sampling interval, as well as the augmented vector and integral terms. Also, the proposed looped-functionals construct two augmented vectors with integral vectors that are zeros at 𝑡� = 𝑡�𝑘� and 𝑡� = 𝑡�𝑘�+1, respectively. By utilizing these two augmented vectors, the looped-functionals fully utilize the sampling patterns compared with the literature. Based on the proposed L-K functionals, this paper derives not only the stability criterion for the NCSs with the transmission delay, but also the stabilization criterion for the NCSs with the transmission delay and the deception attack in terms of linear matrix inequalities (LMIs), respectively. Numerical example demonstrates the validity of the proposed approach.