Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented....

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2018-09, Vol.48 (9), p.2736-2749
Main Authors: Jinghao Li, Qingling Zhang, Xing-Gang Yan, Spurgeon, Sarah K.
Format: Article
Language:English
Subjects:
Control stability
Control systems
Fuzzy control
Fuzzy systems
Integral sliding mode control
Integrals
inverted pendulum
Linear matrix inequalities
Lyapunov methods
Mathematical models
Matrix methods
Motion stability
nonparallel distributed compensation (Non-PDC)
Robust stabilization
Robustness
Robustness (mathematics)
Sliding mode control
Stability analysis
Stochastic processes
Stochastic systems
Symmetric matrices
Takagi–Sugeno (T–S) fuzzy stochastic descriptor systems
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Summary:This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2017.2749244