Stability Analysis and Stabilization of General Conformable Polynomial Fuzzy Models with Time Delay

• Published in: Symmetry (Basel) 2024-10, Vol.16 (10), p.1259
• Main Authors: Iben Ammar, Imen, Gassara, Hamdi, Rhaima, Mohamed, Mchiri, Lassaad, Ben Makhlouf, Abdellatif
• Format: Article
• Language: English
• Subjects: Algorithms; Effectiveness; Functionals; Fuzzy systems; general conformable system; Linear matrix inequalities; Lyapunov–Krasovskii functional; Nonlinear systems; polynomial fitting approximation; polynomial model; Polynomials; S-O-Ss approach; Stability analysis; time delay; Time lag
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym16101259

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we establish SAS conditions for these models using a Lyapunov–Krasovskii functional and the S-O-S approach, making the SAS conditions in this work less conservative than the Linear Matrix Inequalities (LMI)-based approach to the T-SF models. In addition, the SAS conditions are found by satisfying S-O-S conditions dependent on membership functions that are reliant on the polynomial fitting approximation algorithm. These S-O-S conditions can be solved numerically using the recently developed SOSTOOLS. To demonstrate the effectiveness and practicality of our approach, two numerical examples are provided to demonstrate the effectiveness and practicality of our approach.