A sampled-data control scheme for fractional-order fuzzy systems via looped-functional

This study aims to address the stability analysis and stabilization of fractional-order Takagi-Sugeno fuzzy systems (FOT-SFS) via the input delay sampled-data control (IDSDC) scheme. For the first time, an improved looped-Lyapunov functional (ILLF) is proposed for FOT-SFS, where the ILLF is constructed as fractional-order and parameter-based, which provides the sampling instant information. The constructed ILLF is also based on a fractional parameter 0<beta<1 associated with the information of split sampling interval, whereas the fractional derivative is based on the fractional parameter 0<alpha <= 1 A new lemma is derived, which is fractional-order-based and fractional-parameter-based. This new lemma helps to find the fractional derivative of ILLF. The sufficient stability criteria for FOT-SFS are established within the framework of linear matrix inequalities. Based on the ILLF and IDSDC with controller gains, the asymptotic stability of FOT-SFS is attained. Finally, numerical examples are constructed to demonstrate the efficacy of the IDSDC scheme and sampled-data conditions.