A polynomial eigenvalue test for checking DLMI constraints. (February 2023) - Baldissera, João Victor Omar; Galvão, Roberto Kawakami Harrop; Gabriel, Gabriela Werner
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.