Graphical L2-stability analysis of Takagi–Sugeno control systems in the frequency domain

• Published in: Fuzzy sets and systems Vol. 171; no. 1; pp. 93 - 105
• Main Authors: Ban, Xiaojun, Gao, X.Z., Huang, Xianlin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 16.05.2011; Elsevier
• Subjects: Applied sciences; Circle criterion; Circuit properties; Computer science; control theory; systems; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Frequency response methods; Graphical [formula omitted] analysis; Information, signal and communications theory; Mathematical methods; Miscellaneous; Small gain theorem; Takagi–Sugeno (T–S) fuzzy control systems; Telecommunications and information theory; Theoretical computing; Graphical L2-stability analysis; Frequency response methods; Takagi–Sugeno (T–S) fuzzy control systems; Circle criterion; Small gain theorem; Fuzzy system; Control system; stability analysis; Continuous time; Fuzzy set; Takagi-Sugeno (T-S) fuzzy control systems; Fuzzy control; Engineering; Upper bound; Sufficient condition; Graphical L; Information processing; Numerical stability
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2011.01.012

In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi–Sugeno (T–S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L2-gain, the L2-stability of the above T–S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T–S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T–S fuzzy system can be graphically examined.