Estimated-State Feedback Fuzzy Compensator Design via a Decentralized Approach for Nonlinear-State-Unmeasured Interconnected Descriptor Systems

• Published in: Processes Vol. 12; no. 1; p. 101
• Main Authors: Chang, Wen-Jer, Su, Che-Lun, Lee, Yi-Chen
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2024
• Subjects: Analysis; Case studies; Compensators; Control systems design; Control theory; Controllers; Convexity; Design; Dynamic stability; Feedback; Feedback control; Fuzzy control; Fuzzy sets; Liapunov functions; Linear matrix inequalities; Mathematical analysis; Methods; Nonlinear control; Ordinary differential equations; Research methodology; Simulation; Simulation methods; Stability analysis; State feedback; Subsystems; Systems stability
• ISSN: 2227-9717; 2227-9717
• DOI: 10.3390/pr12010101

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability.