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Title: On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case
Authors: Liang, J
Wang, Z
Liu, X
Keywords: Stochastic;Discrete-time fuzzy system;Lyapunov functiona;Linear Matrix Inequality (LMI);Passivity;Disturbance;Time-varying delay
Issue Date: 2010
Publisher: IEEE
Citation: IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 40(3): 964 - 969, Jun 2010
Abstract: Takagi–Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.
Description: Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
ISSN: 1083-4419
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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