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Type: Journal article
Title: Stability and stabilization of a class of discrete-time fuzzy systems with semi-Markov stochastic uncertainties
Author: Zhang, L.
Yang, T.
Shi, P.
Liu, M.
Citation: IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 2016; 46(12):1642-1653
Publisher: IEEE
Issue Date: 2016
ISSN: 1083-4427
Statement of
Lixian Zhang, Ting Yang, Peng Shi, and Ming Liu
Abstract: This paper addresses the problems of stability and stabilization for a class of discrete-time Takagi–Sugeno fuzzy systems with semi-Markov stochastic uncertainties. By means of the semi-Markov kernel, the probability density function of the sojourn time for different modes in describing the underlying semi-Markov stochastic uncertainties can be mode-dependent in contrast with the previous studies. Both the sojourn-timeindependent and sojourn-time-dependent Lyapunov functions are proposed, by which the stability criteria are obtained in terms of a new σ-error mean square stability concept, and the latter is demonstrated to be less conservative and more practical than some existing results. Then, control synthesis problem is investigated and the sufficient conditions on the existence of admissible mode-dependent state-feedback stabilizing controller are developed. A numerical example and a cart-pendulum system are given to show the effectiveness and potential of the new design techniques.
Keywords: σ-error mean square stability; semi-Markov stochastic uncertainties; Takagi–Sugeno (T–S) fuzzy system
Description: Date of publication March 7, 2016; date of current version November 15, 2016.
Rights: © 2016 IEEE.
DOI: 10.1109/TSMC.2016.2527627
Grant ID: 61021002
HIT.BRET IV.201306
Published version:
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Electrical and Electronic Engineering publications

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