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Robust finite-time and fixed-time bipartite consensus problems for multi-agent systems via discontinuous protocol

This paper addresses the robust finite-time and fixed-time bipartite consensus problems for multi-agent systems under the signed graphs. A unified discontinuous control protocol is constructed to achieve both finite-time bipartite consensus (FINBC) and fixed-time bipartite consensus (FIXBC) only by adjusting the parameters, regardless of whether the signed graph is structurally balanced or unbalanced. By using discontinuous techniques, some simple sufficient conditions for FINBC/FIXBC are provided; moreover, the upper bounds of the settling times are explicitly estimated. Simulations show that the proposed control protocols are effective.