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

Authors:
Xiaojun Ban;X. Z. Gao;Xianlin Huang
Affiliations:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, PR China;Department of Automation and Systems Technology;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, PR China
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

In this paper, the upper bound of the L"2-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 L"2-gain, the L"2-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 L"2-stability of certain kind of T-S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L"2-stability of the simplified continuous-time T-S fuzzy system can be graphically examined.