Stability of Takagi-Sugeno systems under nonvanishing disturbances: estimating inescapable sets

Abstract

The present work analizes the behaviour of Takagi-Sugeno fuzzy systems in front of non-vanishing disturbances (characterized by known amplitude or quadratic-mean power bounds). Such analysis is focused in validating that, in front of a specific disturbance bound and an initial-condition region, there exist an inescapable region (contained in the region where the TS model is valid as a model of the underlying nonlinear system). Some of the stated problems here are cast as linear matrix inequality problems (LMI), efficiently solvable by semidefinite programming. Others, however, will involve nonconvex products of decision-variable matrices and two scalars (BMI), which are solved in an iterative way.

Keywords

• Takagi-Sugeno
• Rechazo a perturbaciones
• Conjunto inescapable
• Estabilidad local
• LMI
• Perturbaciones persistentes