Numerical robust stability analysis of fuzzy feedback linearization regulator based on linear matrix

Abstract

A numerical robust stability analysis for the fuzzy feedback linearisation regulator is presented using linear matrix inequalities (LMI) theory. The well known Takagi–Sugeno fuzzy model is used as the nonlinear plant model. Uncertainty is assumed to be included in the model structure with known bounds. For this structured uncertainty, the closed system can be cast into a Lur'e system by a simple transformation. From the LMI stability condition for the Lur'e system, we can derive the robust stability condition for the fuzzy feedback linearisation regulator based on the Takagi–Sugeno fuzzy model. The effectiveness of the proposed analysis is illustrated by a computer simulation.