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

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–Sugeno (T–S) fuzzy systems, time-delay.

Article

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.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

Stats or Metrics

Share this article on

  • line

Related articles in IJCAS

IJCAS

eISSN 2005-4092
pISSN 1598-6446