Resilient Consensus for Discrete-Time Multi-agent Systems with Dynamic Leader and Tolerance to Node Failure

This paper investigates the resilient consensus problems for discrete-time multi-agent systems (MASs) with malicious agents, dynamic leader, and node failure. A resilient controller is proposed to counteract the impact of malicious agents. And sufficient conditions, especially on graph robustness, are derived for achieving consensus with ultimately bounded error. To deal with node failure that can occur in engineering practice and disrupt network topology, a concept called \(r^s\) -LF graphs is introduced to describe robust graphs tolerant to limited node failure. Methods for constructing elemental \(r^s\) -LF graphs and combining them to form larger ones are provided. Simulations with comparison to a classical controller are conducted to validate the theoretical results.