Stability and Stabilization of Takagi–Sugeno Fuzzy Second-Fractional-Order Linear Networks via Nonreduced-Order Approach
研究了Takagi-Sugeno模糊二阶分数阶时滞线性网络的全局渐近稳定性与镇定问题，设计了模糊状态反馈和自适应控制方法，所有结果均基于非降阶方法直接证明。
The extensively studied fractional-order dynamical networks only contain a uniform fractional derivative, which restricts the scope of fractional-order investigation. One type of Takagi–Sugeno fuzzy second-fractional-order linear networks is established in this article. First, by defining a novel Lyapunov functional, a sufficient criterion is offered to ensure global asymptotic stability of the addressed networks with time delay. Second, a fuzzy state-feedback control scheme is designed for the Takagi–Sugeno fuzzy second-fractional-order delayed linear networks to achieve global stabilization. Third, considering that only a few scholars have worked on adaptive control of fractional-order networks, an adaptive control method is also designed to realize the global stabilization of the Takagi–Sugeno fuzzy second-fractional-order linear networks, which does not contain the sign function and chattering problem can be averted. All results, given as algebraic criteria, are proved directly from the Takagi–Sugeno fuzzy second-fractional-order networks without utilizing the reduced-order approach. Three simulation examples are conducted to show the validity of the theoretical results at last.