An LMI framework for addressing the control of time‐delayed fuzzy descriptor systems via sliding mode techniques

Summary This study addresses the issue of developing an adaptive combined integral fuzzy sliding mode (ACIFSM) control for a class of time‐delay nonlinear descriptor systems represented by Takagi–Sugeno (TS) fuzzy models through the linear matrix inequality (LMI) framework. The systems being investigated are susceptible to both exogenous disturbances and uncertainties. The systems under study are subject to uncertainties as well as exogenous disturbances. The matched uncertainty is represented in a uniform structure that can be adjusted using the adaption laws. By adopting a novel fuzzy sliding manifold with a time‐delay that is based on a LMI, it is proved that the resulting closed‐loop system can ensure the reaching condition, hence ensuring its stability. According to the constructed fuzzy sliding manifold, a novel ACIFSM controller is proposed, and its structure is determined by the adaptive laws and the control input matrices. Finally, two examples are provided to demonstrate the validity of the methods employed in this research.