Observer-Based Interval Type-2 L<sub>2</sub> – L<sub>∞</sub>/H<sub>∞</sub> Mixed Fuzzy Control for Uncertain Nonlinear Systems Under Measurement Outliers
Zhenxing Zhang, Jiuxiang Dong
Abstract
In this article, the observer-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L}_{\infty }/ \mathcal {H}_{\infty }$ </tex-math></inline-formula> mixed control issue for uncertain nonlinear plants in the presence of measurement outliers is investigated under interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy approach. Through using lower and upper membership functions, the uncertainties that exist in nonlinear systems can be captured efficaciously. For the sake of reducing the effect of abrupt abnormal signals that disturb the measurements utilized for the purpose of state estimation, a novel fuzzy observer is designed via utilizing the adaptive saturation of output errors. After that, sufficient conditions are derived to ensure the exponential stability with a mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}- \mathcal {L}_{\infty }/\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance level of considered systems on the basis of Lyapunov stability theory. Finally, the usefulness of the new designed control approach is confirmed through two demonstrative simulation examples.