Robust H∞ control with D-stability via static output feedback for nonlinear active suspension systems

Abstract

This paper proposes a static output feedback (SOF) design for $\mathcal{D}$-stabilization, disturbance attenuation via $\mathcal{H}_{\infty}$ norm, and controller norm constraint for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. The objective is to ensure that the closed-loop system eigenvalues remain within a predefined circular region, guaranteeing a minimum decay rate. Simultaneously, the $\mathcal{H}_{\infty}$ approach mitigates the effects of uncertainties and external disturbances. Additionally, a constraint on the controller gain norm is imposed to prevent excessively high gains that could hinder practical implementations. The proposed methodology relies on a matrix decomposition, enabling the static output feedback solution to be derived from a corresponding state feedback solution. The proposed approach is applied to an active suspension system, highlighting its feasibility and performance.