Feedback Control Design Strategy for Stabilization of Delayed Descriptor Fractional Neutral Systems with Order 0 ϱ 1 in the Presence of Time-Varying Parametric Uncertainty

• Published in: Fractal and fractional Vol. 8; no. 8; p. 481
• Main Authors: Aghayan, Zahra Sadat, Alfi, Alireza, Pahnehkolaei, Seyed Mehdi Abedi, Lopes, António M
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-08-2024
• Subjects: Closed loops; Control methods; Control stability; Control systems; Control theory; Controllers; descriptor system; Differential equations; Euclidean space; Feedback control; fractional-order; Linear matrix inequalities; neutral delay; Output feedback; regularity; Robotics; Robust control; Stability analysis; Stability criteria; stabilization; Systems design; Time varying control; Uncertainty; Germany
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract8080481

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature.