https://doi.org/10.1140/epjs/s11734-024-01328-7
Regular Article
A sampled-data control scheme for fractional-order fuzzy systems via looped-functional
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 600127, Chennai, Tamil Nadu, India
Received:
29
April
2024
Accepted:
7
September
2024
Published online:
24
September
2024
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 
, associated with the information of split sampling interval, whereas the fractional derivative is based on the fractional parameter 
. 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.
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