Robust Static Output Feedback $\mathcal {H}_\infty$ Control for Uncertain Takagi–Sugeno Fuzzy Systems

Abstract

In this work, a robust static output feedback (SOF) design for continuous-time nonlinear systems under norm bounded uncertainties, described as a Takagi–Sugeno (TS) system is proposed. The key features are that a switching control law is used to activate the SOF gains to stabilize the uncertain TS fuzzy system and the SOF design does not require the measurements of all premise variables in real time as in the standard fuzzy parallel distributed compensation design. The main result is given in terms of linear matrix inequalities, which guarantees a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$</tex-math></inline-formula> attenuation level of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> for the SOF control system. The efficiency of the main results is illustrated with examples, including a nonlinear active suspension system under uncertain driver masses, and compared with other published results from the literature.