Local Non-Quadratic Robust Tracking Control for Takagi-Sugeno systems: A D-stability design

This study focuses on the synthesis of robust tracking control for nonlinear systems characterized by uncertain and disturbed Takagi-Sugeno multiple models, integrating D-stability constraints with ${\mathcal{L}_2}$-gain performance. D-stability is ensured by confining the closed-loop eigenvalues within a predefined LMI region, while ${\mathcal{L}_2}$-gain analysis reduces the impact of model uncertainties and external disturbances. To this end, relaxed sufficient LMI conditions based on a poly-quadratic fuzzy Lyapunov function are derived. The proposed approach is validated through a simulation of an inverted pendulum system.