A Balanced Model Reduction for T-S Fuzzy Systems with Uncertain Time Varying Parameters

摘要

This paper deals with a balanced model reduction for a class of Takagi-Sugeno(T-S) fuzzy systems with uncertain time varying parameters. We define a generalized controllability Gramian and a generalized observability Gramian for quadratically stable T-S fuzzy systems with uncertainties. We introduce a balanced state space realization using the generalized controllability and observability Gramians and obtain a reduced model by truncating not only states but also time varying uncertain parameters from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability and observability Gramians can be computed from solutions of linear matrix inequalities(LMI's).