Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and c...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2000-04, Vol.8 (2), p.200-211
Main Authors: Yong-Yan Cao, Frank, P.M.
Format: Article
Language:English
Subjects:
Control design
Delay effects
Dynamical systems
Fuzzy
Fuzzy control
Fuzzy logic
Fuzzy reasoning
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Mathematical models
Nonlinear dynamics
Nonlinear systems
Nonlinearity
Stability analysis
State feedback
Takagi-Sugeno model
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Summary:Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.
ISSN:1063-6706
1941-0034
DOI:10.1109/91.842153