A polynomial eigenvalue test for checking DLMI constraints. (February 2023)

• Record Type: Journal Article
• Authors: Baldissera, João Victor Omar; Galvão, Roberto Kawakami Harrop; Gabriel, Gabriela Werner
• Is Part Of: Automatica. Volume 148(2023)
• Publication Date: 2023-02
• Subjects: Differential Linear Matrix Inequalities -- Polynomial eigenvalues -- Sampled-data control -- Optimization-based controller synthesis; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110729
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In order to obtain an optimization problem with a finite number of variables and constraints, Differential Linear Matrix Inequalities (DLMIs) are usually recast into the form of a system of LMIs. To this end, a typical approach consists in parameterizing the solution as a linear combination of known functions, with weights to be optimized. The constraints are then imposed on a finite set of discrete time points. This technical communiqué is concerned with the problem of checking whether a matrix polynomial solution obtained in this manner satisfies the original DLMI constraints. To this end, a novel test based on the concept of polynomial eigenvalues is presented. The proposed test is illustrated through a numerical example based on the H ∞ synthesis of a sampled-data controller.