Bipartite Output Synchronization of Fuzzy Fractional Output-Coupled Networks via Membership Function-Dependent Adaptive Control

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This article focuses on the bipartite output synchronization for a type of fuzzy fractional output-coupled networks based on fractional-order fuzzy adaptive strategies. Firstly, in view of the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in reality, a class of T-S fuzzy fractional networks with output couplings is established under the signed graph framework. Next, a type of membership function-dependent fractional adaptive schemes is presented to automatically regulate the control gains, some criteria of bipartite output synchronization are derived based on the characteristic of the signed topology instead of traditional gauge transformation method. Particularly, a pinning adaptive control scheme is employed to investigate bipartite output synchronization for fuzzy fractional output-coupled networks with the positive-definite output matrix, which determines the pinning nodes just dependent of the cooperative links among nodes in signed graph. The developed criteria are finally confirmed by some examples.