Robust static output feedback fuzzy control design for nonlinear systems with persistent bounded disturbances: A singular value decomposition approach

Abstract

This study introduces L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -gain static output feedback fuzzy control design for nonlinear systems via T-S fuzzy models. Unlike the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> ) control case, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -gain control problem is dealing with persistent bounded disturbances. The structure of static output feedback controller is much simpler than that of dynamic output feedback controller. A singular value decomposition (SVD) method is proposed to solve the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -gain static output feedback fuzzy control problem. By the proposed SVD method, the problem of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -gain static output feedback fuzzy control design for nonlinear systems is characterized in terms of solving a linear matrix inequality problem (LMIP) if some scalars are specified in advance.