New Results on Interval Type-3 Fuzzy Control for Nonlinear Time-Delay Systems Using Convex Relaxation Technique

Abstract

In this article, the interval type-3 fuzzy-based state feedback control is proposed for the stabilization problem of interval type-3 fuzzy systems (IT3FSs) subject to time-varying delay. Specifically, to improve the model accuracy and control capabilities, we proposed a nonparallel distributed compensation-based controller approach, be precise, the system and controller adopts the distinct membership functions. Moreover, the stability analysis of IT3FSs in the state space form is studied newly in this article. Besides the primary membership function that exists for interval type-2 fuzzy systems (IT2FSs), the IT3FSs possess the secondary membership function to handle the overall uncertainty which enacts the superiority of the proposed work. Notably, the adequate stability criteria are derived in the form of linear matrix inequality (LMI) using the Lyapunov stability theorem. Additionally, the convex relaxation technique is used to strengthen the design flexibility and achieve the faster convergence rate, which converts an optimization problem with a vector variable to a convex program with a matrix variable, via a lifting technique. A noteworthy aspect is that the application of the convex relaxation technique in the context of IT3FSs is proposed for the first time in literature. Finally, the comparative results between IT2FSs and IT3FSs are shown via two illustrative examples, including the inverted-pendulum model, to underscore the efficacy and practical implementations of the developed control methodology.