H∞ Filtering for Discrete-Time Singular Markov Jump Systems Under DoS Attacks and Its Application

This study addresses $\mathcal {H}_{\infty }$ filtering against DoS attacks within the framework of singular Markov jump systems. To provide a more comprehensive depiction of the issue pertaining to cyber security, DoS attacks are perceived as occurring in an unpredictable manner and can be represented by a collection of a random variable that follows the Bernoulli distribution. Consequently, the corresponding filter error system is formulated. Utilizing a set of viable linear matrix inequalities, this research establishes criteria of stochastically admissible for filter error system, ensuring a specified $\mathcal {H}_{\infty }$ performance. A filter design method under DoS attacks is proposed. Finally, the effectiveness of this method is demonstrated through a practical example involving a tunnel diode model.