Regular Papers
International Journal of Control, Automation and Systems 2015; 13(4): 986-994
Published online May 23, 2015
https://doi.org/10.1007/s12555-014-0327-6
© The International Journal of Control, Automation, and Systems
LMI Conditions for Local Stability and Stabilization of Continuous-Time T–S Fuzzy Systems
In this paper, we propose linear matrix inequality (LMI) formulations to analyze local stability and design controllers that locally stabilize continuous-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems. In order to estimate the domain of attraction (DA), the so-called fuzzy Lyapunov function is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. Quadratic bounds on the time-derivative of the membership functions are employed to derive the main results. Finally, examples are given to illustrate the proposed methods.
Keywords Domain of attraction, linear matrix inequality (LMI), Lyapunov function, nonlinear systems, Takagi–Sugeno (T–S) fuzzy systems.
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Regular Papers
International Journal of Control, Automation and Systems 2015; 13(4): 986-994
Published online August 1, 2015 https://doi.org/10.1007/s12555-014-0327-6
Copyright © The International Journal of Control, Automation, and Systems.
LMI Conditions for Local Stability and Stabilization of Continuous-Time T–S Fuzzy Systems
Dong Hwan Lee, Young Hoon Joo*, and Myung Hwan Tak
Kunsan National University
Abstract
In this paper, we propose linear matrix inequality (LMI) formulations to analyze local stability and design controllers that locally stabilize continuous-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems. In order to estimate the domain of attraction (DA), the so-called fuzzy Lyapunov function is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. Quadratic bounds on the time-derivative of the membership functions are employed to derive the main results. Finally, examples are given to illustrate the proposed methods.
Keywords: Domain of attraction, linear matrix inequality (LMI), Lyapunov function, nonlinear systems, Takagi–,Sugeno (T–,S) fuzzy systems.
Vol. 23, No. 3, pp. 683~972
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