A Novel relaxation of the static output feedback problem for a class of plants

• Published in: Automatica (Oxford) 2023-12, Vol.158, p.111285, Article 111285
• Main Author: August, Elias
• Format: Article
• Language: English
• Subjects: Bilinear matrix inequality; Convex relaxation; Semidefinite programming; Stability; Static output feedback
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2023.111285

The static output feedback control problem is important, as it is concerned with the case when one cannot measure all state variables. It seeks to obtain a stabilising control under these conditions and is, often, difficult to solve. For a certain class of linear dynamical systems, we provide a novel approach to obtain a stabilising control gain matrix. The class of plants considered is of those, for which we can measure at least half of all state variables and where those measurements affect at least half of all state variables. Moreover, when we write the (linearly transformed) system matrix in block form, we require that either the two lower block matrices are nonsingular, or, if the inputs affect the measured state variables directly, at least the lower left one is nonsingular. We then show that we can determine the stabilising control gain matrix from the solution of a linear matrix inequality. Finally, we apply the approach to different benchmark problems, where it performs well, and confirm its good performance through additional numerical experiments.