L2–L∞ Output Feedback Controller Design for Fuzzy Systems over Switching Parameters

Xiaojie SU; Fengqin XIA; Yong-Duan SONG; Michael V. BASIN; Ling ZHAO

doi:10.1109/TFUZZ.2018.2848652

L₂–L_∞ Output Feedback Controller Design for Fuzzy Systems over Switching Parameters

Xiaojie SU^*
, Fengqin XIA
, Yong-Duan SONG
, Michael V. BASIN
, Ling ZHAO

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

32 Citations (Scopus)

Abstract

This paper focuses on the problem of L₂–L_∞ dynamic output feedback controller (DOFC) design for nonlinear switched systems with nonlinear perturbations in the Takagi-Sugeno fuzzy framework. First, the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law. Then, based on the technique of piecewise Lyapunov functions, a fuzzy-rule-dependent DOFC is designed to ensure that the overall closed-loop system is exponentially stable with a weighted L₂–L_∞ performance level (γ,α). The solvability condition for the desired DOFC is derived using a linearization technique. It is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software. Finally, two simulation examples illustrate effectiveness of the developed technique, including cognitive-radio systems.

Original language	English
Pages (from-to)	3755-3769
Number of pages	15
Journal	IEEE Transactions on Fuzzy Systems
Volume	26
Issue number	6
Early online date	18 Jun 2018
DOIs	https://doi.org/10.1109/TFUZZ.2018.2848652
Publication status	Published - Dec 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 1993-2012 IEEE.

Funding

This work was supported in part by the Graduate Research and Innovation Foundation of Chongqing, China (CYS17047); in part by the National Natural Science Foundation of China under Grant 61772095 and Grant 61304104; in part by the Fundamental Research Funds for the Central Universities (2018CDQYZDH0040); and in part by the Science and Technology Research Project of Chongqing Municipal Education Commission under Grant KJ1600518. The work of M. V. Basin was supported in part by the Mexican National Science and Technology Council (CONACyT) under Grant 250611 and in part by the Government of Russian Federation under Grant 08-08.

Keywords

Fuzzy control systems
output feedback control (OFC)
relaxed stability analysis

Access to Document

10.1109/TFUZZ.2018.2848652

Cite this

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title = "L2–L∞ Output Feedback Controller Design for Fuzzy Systems over Switching Parameters",

abstract = "This paper focuses on the problem of L2–L∞ dynamic output feedback controller (DOFC) design for nonlinear switched systems with nonlinear perturbations in the Takagi-Sugeno fuzzy framework. First, the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law. Then, based on the technique of piecewise Lyapunov functions, a fuzzy-rule-dependent DOFC is designed to ensure that the overall closed-loop system is exponentially stable with a weighted L2–L∞ performance level (γ,α). The solvability condition for the desired DOFC is derived using a linearization technique. It is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software. Finally, two simulation examples illustrate effectiveness of the developed technique, including cognitive-radio systems.",

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