Cyber secure consensus of fractional order multi-agent systems with distributed delays: Defense strategy against denial-of-service attacks

Abstract

Leader-follower cyber secure consensus problem in cybersecurity is crucial as it directly addresses the need for secure and stable communication in a networked system, which is paramount in safeguarding against cyber threats like denial-of-service attacks. In this article, by utilizing control strategy with distributed delays in denial-of-service attack's presence for discrete-time multi-agent system of fractional-order, the leader-following cyber secure consensus problem is examined. Nonlinear functions have been assumed in the leader and follower equation of the system to study variations due to this function in the system. As multi-agent system is networked environment, in response to numerous threats, their security control becomes critically desirable, for example, denial of service. The consensus performance may be destabilized by resulting topologies which are caused by Denial-of-Service attacks. The connectivity between agents is destroyed, especially under connectivity-broken attacks. In order to overcome these problems, the strategy of novel defense which consists of consensus (with distributed delays) control is introduced. By using Caputo fractional difference operator sufficient criteria which includes the condition in terms LMI is derived and by using Lyapunov function approach, average dwell time and algebraic graph theory for security of addressed system's cyber secure consensus this is done for determining the obtained system of error's stability. Finally, by showing some numerical examples on the introduced systems, the effectiveness of the obtained results is determined.