Abstract
In this paper, the consensus of fractional-order Takagi-Sugeno fuzzy multi-agent systems with time delay is studied. First, the fractional-order Barbaˇlat lemma is proposed to explore fractional-order systems by using the integer-order Lyapunov method. In addition, the adaptive controllers with and without an input time delay are designed to ensure consensus of fractional-order Takagi-Sugeno fuzzy multi-agent systems with time delay. Next, a class of new Lyapunov-Krasovskii functions is constructed that utilize time delay information, unlike the previous functions. Then, based on the designed adaptive controls and the constructed Lyapunov-Krasovskii functions, some consensus criteria are proposed to guarantee consensus of fractional-order Takagi-Sugeno fuzzy multi-agent systems with time delay. Finally, three examples are given to verify the correctness and effectiveness of the proposed methods.
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