Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

Abstract The robust $$H_\infty$$ H ∞ observer-based control design is addressed here for non-linear Takagi-Sugeno (T-S) fuzzy systems with time-varying delays, subject to uncertainties and external disturbances. This motivated by the quadruple-tank time delay problem. observer methodology based on constructing an appropriate Lyapunov–Krasovskii functional (LKF) augmented system formed from original delayed states. bilinear terms are transferred linear matrix inequalities, thanks a change of variables which can be solved in one step. Furthermore, employing $$\mathcal {L}_2$$ L 2 performance index, adverse effects persistent bounded disturbances largely avoided. proposed method has advantage relating controller Lyapunov function both Then, gains obtained simultaneously solving these inequalities off-the-shelf software (Yalmip/MATLAB toolbox). Finally, application simulated carried out demonstrate benefits technique, showing compromise between simplicity robustness that outperforms previous approaches.