An element-wise linear matrix inequality approach for output regulation problems

Output regulation theory is a powerful tool for trajectory tracking of nonlinear systems which has led to extensive research for more than two decades, due to its mathematical insight, elegance, and effectiveness of solutions. Despite its success, regulation relies mainly on the designer´s ability to fit the existence results and conditions for controller design. This paper provides a systematic approach to solve the output regulation problem via state- or error-feedback; this approach is fully based on element-wise linear matrix inequalities which are numerically solvable by interior-point-based methods and implemented in commercially available software.