Analyzing Linear Matrix Inequality for Stability Control of Inverted Pendulum on a Cart

This article presents the application of linear matrix inequalities (LMIs) in Takagi-Sugeno (T-S) fuzzy control for the stabilization of an inverted pendulum on a cart. This control technique, utilizing fuzzy if-then rules and local linear models, enables precise control under diverse operating conditions. On the other hand, LMIs provide a powerful framework for analyzing and designing control systems, ensuring robust stability and performance through a set of linear inequalities. The Yalmip toolbox, a MATLAB-based optimization modeling language, facilitates the use of LMIs in control system design. In this study, LMI theorem with two relaxation lemmas are presented and compared in terms of computational complexity. The effectiveness of the Takagi-Sugeno fuzzy control combined with LMI-based control methods is demonstrated in achieving stable control with good performance, offering promising avenues for control strategies in various practical applications.