A balanced model reduction for T-S fuzzy systems with integral quadratic constraints

Abstract

This paper deals with a balanced model reduction for a class of nonlinear systems with integral quadratic constraints(IQC's) using a T-S(Takagi-Sugeno) fuzzy approach. We define a generalized controllability Gramian and a generalized observability Gramian for a stable T-S fuzzy systems with IQC's. We obtain a balanced state space realization using the generalized controllability and observability Gramians and obtain a reduced model by truncating not only states but also IQC's from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability Gramian and observability Gramian can be computed from solutions of linear matrix inequalities. © Springer-Verlag Berlin Heidelberg 2005.