Regular Papers
International Journal of Control, Automation and Systems 2016; 14(1): 29-38
Published online February 11, 2016
https://doi.org/10.1007/s12555-015-2006-7
© The International Journal of Control, Automation, and Systems
Local Stability and Local Stabilization of Discrete-Time T–S Fuzzy Systems with Time-delay
The goal of this paper is to propose linear matrix inequality (LMI) formulations to analyze the local stability and local stabilization of discrete-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems with time-delay. In order to estimate the domain of attraction (DA) of the time-delay systems, the so-called fuzzy Lyapunov-Krasovskii functionals are used to characterize the subsets of the DA as sublevel sets of the Lyapunov- Krasovskii functionals. We use the information of the variation rates of the membership functions to obtain less conservative results. Finally, examples are given to illustrate the proposed methods."
Keywords Domain of attraction, Lyapunov function, nonlinear systems, Takagi–Sugeno (T–S) fuzzy systems, time-delay.
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Regular Papers
International Journal of Control, Automation and Systems 2016; 14(1): 29-38
Published online February 1, 2016 https://doi.org/10.1007/s12555-015-2006-7
Copyright © The International Journal of Control, Automation, and Systems.
Local Stability and Local Stabilization of Discrete-Time T–S Fuzzy Systems with Time-delay
Donghwan Lee, Young Hoon Joo*, and In-Ho Ra
Kunsan National University
Abstract
The goal of this paper is to propose linear matrix inequality (LMI) formulations to analyze the local stability and local stabilization of discrete-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems with time-delay. In order to estimate the domain of attraction (DA) of the time-delay systems, the so-called fuzzy Lyapunov-Krasovskii functionals are used to characterize the subsets of the DA as sublevel sets of the Lyapunov- Krasovskii functionals. We use the information of the variation rates of the membership functions to obtain less conservative results. Finally, examples are given to illustrate the proposed methods."
Keywords: Domain of attraction, Lyapunov function, nonlinear systems, Takagi&ndash,Sugeno (T&ndash,S) fuzzy systems, time-delay.
Vol. 23, No. 3, pp. 683~972
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