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LMI Conditions for Local Stability and Stabilization of Continuous-Time T–S Fuzzy Systems

Dong Hwan Lee, Young Hoon Joo*, and Myung Hwan Tak
International Journal of Control, Automation, and Systems, vol. 13, no. 4, pp.986-994, 2015

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.

Keyword : Domain of attraction, linear matrix inequality (LMI), Lyapunov function, nonlinear systems, Takagi–Sugeno (T–S) fuzzy systems.

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