Robust $${H_\infty }$$ H ∞ Filtering for Semi-Markov Jump Systems Encountering Denial-of-Service Jamming Attacks

This study focuses on the issue of $${H_\infty }$$ filtering for discrete-time semi-Markov jump systems encountering denial-ofservice jamming attacks. The semi-Markov kernel, which describes the switching of the system, is determined by the sojourn-time probability density functions and the transition probability. A Bernoulli distribution white sequence is introduced to describe the phenomenon while accounting for the DoS jamming attacks and channel inherent factors on packet dropout. Considering that the DoS jammer has limited energy, it adopts a random attack strategy, and each work cycle and attack period are different. Based on the mean-square stability criterion, a sufficient condition is provided, and the filter is designed to ensure that the filtering error system is stable with the $${H_\infty }$$ performance index. Two examples, including a cognitive radio system, are provided to demonstrate the effectiveness of the proposed filtering method.