Common errors on using convex modelling and linear matrix inequalities for nonlinear control

This note discusses common errors on using convex modelling and linear matrix inequalities for nonlinear control, a methodology that has become increasingly popular due to its systematicness and numerical implementability. Illustrations on common problems are made from existing literature: they are classified and discussed; advices are given to prevent them. Convex modelling is employed in linear parameter varying, Takagi-Sugeno models, and other convex structures in order to subsume or rewrite a nonlinear system for analysis or design via the direct Lyapunov method. Convexity plays a central role in allowing a finite set of vertex conditions in the form of linear matrix inequalities to be sufficient for the corresponding task. In contrast with other nonlinear methodologies, this one produces expressions resembling linear results, which makes it easier to grasp while often inducing subtle mistakes.