Stability Criteria for Fuzzy-Based Sampled-Data Control Systems via a Fractional Parameter-Based Refined Looped Lyapunov Functional

This article is concerned with the stability analysis for the fuzzy-based sampled-data control (SDC) systems, which is based on a fractional parameter-based refined looped-Lyapunov functional (RLLF). To do this, with the help of the Takagi–Sugeno fuzzy method, a SDC can be designed. To derive sufficient criteria, a RLLF with information about the sampling period is proposed. In the RLLF, a fractional parameter is introduced and it has more information on the splitted sampling intervals and delayed states with a fractional parameter. The derived criteria guarantee the asymptotic stability of the proposed system with a
$H_{\infty }$
attenuation level. To validate the derived conditions, a state-space model of nonlinear permanent magnet synchronous motor is proposed. Besides, comparison examples are conducted for analyzing the less conservatism of the merit of the proposed methods. Finally, the simulation outcomes are illustrated the superiority of the work.