A Fuzzy Lyapunov-Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems

Han Sol Kim; Jin Bae Park; Young Hoon Joo

doi:10.1109/TFUZZ.2016.2637368

A Fuzzy Lyapunov-Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems

Han Sol Kim, Jin Bae Park, Young Hoon Joo

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov-Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations.

Original language	English
Article number	7778118
Pages (from-to)	366-373
Number of pages	8
Journal	IEEE Transactions on Fuzzy Systems
Volume	26
Issue number	1
DOIs	https://doi.org/10.1109/TFUZZ.2016.2637368
Publication status	Published - 2018 Feb

Bibliographical note

Funding Information:
Manuscript received May 4, 2016; revised September 27, 2016; accepted November 14, 2016. Date of publication December 8, 2016; date of current version February 1, 2018. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1A6A1A03013567) and by the Korea government (MEST) (NRF-2015R1A2A2A05001610).

Funding Information:
This work was supported by the Basic ScienceResearch Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education (NRF-2016R1A6A1A03013567) and bythe Korea government (MEST) (NRF-2015R1A2A2A05001610).

Publisher Copyright:
© 1993-2012 IEEE.

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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title = "A Fuzzy Lyapunov-Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems",

abstract = "This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov-Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations.",

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note = "Funding Information: Manuscript received May 4, 2016; revised September 27, 2016; accepted November 14, 2016. Date of publication December 8, 2016; date of current version February 1, 2018. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1A6A1A03013567) and by the Korea government (MEST) (NRF-2015R1A2A2A05001610). Funding Information: This work was supported by the Basic ScienceResearch Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education (NRF-2016R1A6A1A03013567) and bythe Korea government (MEST) (NRF-2015R1A2A2A05001610). Publisher Copyright: {\textcopyright} 1993-2012 IEEE.",

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A Fuzzy Lyapunov-Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems

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