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Quadratic stability analysis of the Takagi-Sugeno fuzzy model. (English) Zbl 0929.93024

Summary: The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system. Application examples on fuzzy models of nonlinear plants advocate the efficiency of the method. The examples demonstrate reduced conservatism compared to norm-based criteria.

MSC:

93C42 Fuzzy control/observation systems
93D21 Adaptive or robust stabilization
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
93B50 Synthesis problems
93D09 Robust stability
90C25 Convex programming

Software:

LMI toolbox
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References:

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