Regular Papers
International Journal of Control, Automation and Systems 2017; 15(4): 1867-1876
Published online June 28, 2017
https://doi.org/10.1007/s12555-016-0307-0
© The International Journal of Control, Automation, and Systems
Local Stability Analysis of T–S Fuzzy Systems Using Second-order Time Derivative of the Membership Functions
This paper addresses the local stability analysis problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Based on the Lyapunov method, the proposed analysis procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. Especially, a generalized Lyapunov function that depends on the membership functions (MFs) and its time derivatives is used. Since the Lyapunov function involves the time derivatives of the MFs, the problem of stability analysis and the estimation of the domain of attraction (DA) cannot be converted into convex problems in general. In this paper, we explore the possibility of using the second-order time derivatives of the MFs to determine the DA. Examples are given to illustrate the proposed method."
Keywords Domain of attraction, Lyapunov function, nonlinear systems, stability, Takagi-Sugeno (T-S) fuzzy systems.
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Regular Papers
International Journal of Control, Automation and Systems 2017; 15(4): 1867-1876
Published online August 1, 2017 https://doi.org/10.1007/s12555-016-0307-0
Copyright © The International Journal of Control, Automation, and Systems.
Local Stability Analysis of T–S Fuzzy Systems Using Second-order Time Derivative of the Membership Functions
Donghwan Lee, Young Hoon Joo*, and Dongran Song*
Kunsan National University
Abstract
This paper addresses the local stability analysis problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Based on the Lyapunov method, the proposed analysis procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. Especially, a generalized Lyapunov function that depends on the membership functions (MFs) and its time derivatives is used. Since the Lyapunov function involves the time derivatives of the MFs, the problem of stability analysis and the estimation of the domain of attraction (DA) cannot be converted into convex problems in general. In this paper, we explore the possibility of using the second-order time derivatives of the MFs to determine the DA. Examples are given to illustrate the proposed method."
Keywords: Domain of attraction, Lyapunov function, nonlinear systems, stability, Takagi-Sugeno (T-S) fuzzy systems.
Vol. 23, No. 3, pp. 683~972
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