H∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults

• Published in: Mathematics (Basel) Vol. 9; no. 18; p. 2203
• Main Authors: Jerbi, Houssem, Kchaou, Mourad, Boudjemline, Attia, Regaieg, Mohamed, Ben Aoun, Sondes, Kouzou, Ahmed
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2021
• Subjects: Algorithms; CCL; Control systems design; Control theory; Controllers; Delay; descriptor systems; Feedback control; Fuzzy control; Fuzzy systems; H-infinity control; Missing data; Nonlinear control; Nonlinear systems; Output feedback; randomly occurred non-linearity; sensor failure; Sensors; Time varying control; Tractor trailers; TS fuzzy model
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9182203

In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.