Regional input-to-state stabilization of fuzzy state-delayed discrete-time systems with saturating actuators

• Published in: Information sciences Vol. 557; pp. 250 - 267
• Main Authors: Silva, Luís F.P., Leite, Valter J.S., Castelan, Eugênio B., de Souza, Carla
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2021
• Subjects: Discrete-time Takagi-Sugeno systems; Fuzzy Lyapunov function; Non-PDC fuzzy controller; Regional ISS; Saturating actuators; State delayed systems; State delayed systems; Non-PDC fuzzy controller; Saturating actuators; Discrete-time Takagi-Sugeno systems; Fuzzy Lyapunov function; Regional ISS
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2020.12.043

We address the regional input-to-state stabilization of discrete-time Takagi-Sugeno fuzzy models under delayed state, saturating actuators, and external energy bounded disturbances. We propose a convex method to design state feedback-based non-parallel distributed compensation, ensuring the fuzzy closed-loop system’s regional stability. Moreover, we introduce a geometrical estimate of the region of attraction in an augmented space, allowing a more extensive set of safe initial sequences. Furthermore, the minimization of the ℓ2-gain from the external disturbance to the controlled output ensures closed-loop performance. Also, we provide optimization procedures allowing the maximization of the estimate of the region of attraction or the disturbance energy tolerance. By employing numerical examples, we compare our approach with similar ones found in the literature, showing our proposal’s efficacy, and its outperform concerning the compared methods.