A discontinuous protocol design for finite-time average consensus

In this paper, a consensus problem for a group of n agents is considered. A switching type protocol, or law, is proposed such that the states of all the agents agree upon an average value in finite-time. Sliding mode principles have been used to achieve finite-time average consensus. Specifically the sliding surface is defined as the set corresponding to consensus, on which the sliding motion is obtained in finite-time. Thus the properties of sliding mode control are exploited and finite-time average consensus is attained. A numerical example is provided to demonstrate the finite time properties of the proposed protocol.