Asynchronous-Switching-Based Distributed Interval Filtering for Positive Markov Jump Linear Systems Under Denial-of-Service Attack

Abstract

This article presents an asynchronous distributed interval filtering method for discrete-time positive Markov jump linear systems (MJLSs) with bounded disturbance under the denial-of-service attack. By designing an asynchronous switching-distributed mechanism that depends on a randomly occurred attack, the proposed positive filter can monitor the real-time range of estimated states against the attack. The filtering error systems are modeled as a class of MJLSs with two attack-dependent Markov chains. Some analysis and design results are derived such that the error systems are positive and stochastically internally stable with satisfied <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain performance. The remote power monitoring in telecommunication systems is used for numerical verification.