Stability analysis of polynomial fuzzy model-based control systems with mismatched premise membership functions through symbolic variables

Hak-Keung Lam

doi:10.1007/978-3-319-34094-4_3

Stability analysis of polynomial fuzzy model-based control systems with mismatched premise membership functions through symbolic variables

Hak-Keung Lam^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter investigates the stability of polynomial fuzzy model-based control systems by treating the membership functions and system states as symbolic variables. The information of membership functions is considered in the stability analysis and brought to the SOS-based stability conditions. Techniques are proposed to introduce slack matrix variables carrying the information of membership functions, including the property of membership functions, boundary information of membership functions and boundary information of premise variables, to the SOS-based stability conditions without increasing much the computational demand. Details of mathematical derivation are shown to help readers follow easily the analysis. A simulation example is given to show how to apply the obtained stability conditions during the control design and demonstrate the merits of the proposed stability analysis results.

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing Switzerland
Pages	61-83
Number of pages	23
Volume	64
DOIs	https://doi.org/10.1007/978-3-319-34094-4_3
Publication status	Published - 2016

Publication series

Name	Studies in Systems, Decision and Control
Volume	64
ISSN (Print)	21984182
ISSN (Electronic)	21984190

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10.1007/978-3-319-34094-4_3

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abstract = "This chapter investigates the stability of polynomial fuzzy model-based control systems by treating the membership functions and system states as symbolic variables. The information of membership functions is considered in the stability analysis and brought to the SOS-based stability conditions. Techniques are proposed to introduce slack matrix variables carrying the information of membership functions, including the property of membership functions, boundary information of membership functions and boundary information of premise variables, to the SOS-based stability conditions without increasing much the computational demand. Details of mathematical derivation are shown to help readers follow easily the analysis. A simulation example is given to show how to apply the obtained stability conditions during the control design and demonstrate the merits of the proposed stability analysis results.",

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language = "English",

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series = "Studies in Systems, Decision and Control",

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Stability analysis of polynomial fuzzy model-based control systems with mismatched premise membership functions through symbolic variables. / Lam, Hak-Keung.
Studies in Systems, Decision and Control. Vol. 64 Springer International Publishing Switzerland, 2016. p. 61-83 (Studies in Systems, Decision and Control; Vol. 64).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AB - This chapter investigates the stability of polynomial fuzzy model-based control systems by treating the membership functions and system states as symbolic variables. The information of membership functions is considered in the stability analysis and brought to the SOS-based stability conditions. Techniques are proposed to introduce slack matrix variables carrying the information of membership functions, including the property of membership functions, boundary information of membership functions and boundary information of premise variables, to the SOS-based stability conditions without increasing much the computational demand. Details of mathematical derivation are shown to help readers follow easily the analysis. A simulation example is given to show how to apply the obtained stability conditions during the control design and demonstrate the merits of the proposed stability analysis results.

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Stability analysis of polynomial fuzzy model-based control systems with mismatched premise membership functions through symbolic variables

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