Stabilization of Sampled-Data Systems with Noisy Sampling Intervals and False Data Injection Attacks

In the presence of noisy sampling intervals, the modeling and stabilization problem for a class of sampled-data systems subject to false data injection is investigated. First, the false data injection attack is modeled as discrete sampling format and the continuous-time system under consideration is converted into a discrete-time system with stochastic parameters. Then, in order to deal with computational difficulties, mathematical expectations of both matrix exponential and integral of matrix exponential function are calculated by Kronecker product operation and the law of total expectation. Based on this, the sampled-data stabilization controller is designed such that the closed-loop system is mean-square exponential stable with a prescribed H
∞
performance under noisy sampling interval. Finally, two illustrative examples are provided to verify the effectiveness of the proposed design algorithm.