Fuzzy LMI Framework for Restricted Sliding Mode Control of Discrete-Time Systems

This paper studies the subject of designing an integrated integral fuzzy sliding mode (IIFSM) controller for a class of uncertain discrete-time (DT) non-linear systems that can be expressed via Takagi-Sugeno fuzzy models. The proposed approach is modified in order to provide a robust controller with improved performance in the presence of disturbances, uncertainties, and restrictions related to the magnitude and rate of the control action. Meanwhile, a novel design framework involving the LMI approach is developed to address restrictions on both the magnitude and rate of control action, meeting the needs of practical applications. The attainment of parameters for the sliding function demonstrates that, through the utilization of an IIFSM controller formulated with LMIs, the ensuing closed-loop system can attain uniformly ultimate boundedness (UUB). Ultimately, the proposed approaches are evaluated using the chaotic Lorenz system to illustrate the superiority of the suggested control strategy.