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Discrete-time Sliding Mode Control for Leader Following Discrete-time Multi-Agent System

Ahstract- This paper presents a discrete-time sliding mode controller for synchronization of linear discrete-time multi-agent system with a reference leader using leader following cooperative design method. The discrete-time multi-agent system is configured with a fixed, undirected graph topology as a global system having one leader and other agents as followers. The sliding surface for global system is proposed and a discrete-time sliding mode controller using Gao's reaching law principle is derived. The proposed consensus protocol ensure that the followers synchronize with leader in finite time. Sufficient condition for synchronization, that is the graph eigenvalues restricted into a unit circular region in the complex plane is derived. The robustness property of proposed controller is also checked by applying a slowly varying disturbance. Finally, a numerical example is presented to endow the efficacy of the proposed methods.