Output Feedback Fuzzy Regressive PI Control of Time-Delay Systems with Nonlinear Delay Input/Output

• Published in: International journal of fuzzy systems Vol. 18; no. 1; pp. 15 - 27
• Main Authors: Chiu, Chian-Song, Liu, Chien-Hung
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2016; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Control systems design; Controllers; Coordinate transformations; Engineering; Fuzzy control; Fuzzy sets; Linear matrix inequalities; Management Science; Mathematical analysis; Mathematical models; Methods; Nonlinear systems; Nonlinearity; Operations Research; Optimization techniques; Output feedback; Proportional integral; Stability analysis; Time delay systems; Time-delay system; Proportional-integral control; Linear matrix inequality (LMI); Output feedback
• ISSN: 1562-2479; 2199-3211
• DOI: 10.1007/s40815-015-0096-2

This paper presents the fuzzy regressive proportional-integral (FRPI) control for the output feedback regulation of uncertain time-delay systems subject to both nonlinear delayed input and output. First, the system is represented in a new fuzzy linear regressive model which does not have input/output nonlinearity and input delay in each fuzzy rule. Based on the fuzzy linear regressive model, the output feedback regulation controller is straightforwardly designed by combining the proportional-integral and regressive compensation. Then, the gain design is performed by Lyapunov–Krasovskii stability analysis and Linear matrix inequality (LMI) conversion. The LMI optimization approach is utilized to avoid iteratively solving bilinear gain conditions. Moreover, no observer is used in this paper. In addition, the FRPI controller can be further reduced to a linear regressive PI controller form for easier implementation. Finally, numerical simulations show the expected performance.