Interpolation With Strictly F-Positive Real Matrix and Application to Strong Stabilization

• 成果类型: Article
• 署名作者: Stefanovski, Jovan
• 署名单位: St. Clement of Ohrid University of Bitola
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3349101
• 发表日期: 2024
• 页码: 4080-4085
• 关键词: Interpolation; Linear matrix inequalities; Eigenvalues and eigenfunctions; control design; Sufficient conditions; Poles and zeros; MIMO communication; strong stabilization

摘要

The necessary and sufficient conditions for the newly introduced problem to find a strictly F-positive real (SF-PR) interpolant for a one-sided rational interpolation are given, as well as the set of all solutions. The SF-PR property of the interpolant H, for a rational matrix (RM) F to be found, implies that H is bistable and biproper (BiPS). Since such an interpolant is needed in the strong stabilization problem, the interpolation result is used to develop a control design algorithm such that a stable stabilizing controller of degree n+l is constructed using the RMs F and H, where l is the number of unstable plant zeros. Examples, including one with a chemical reactor plant, illustrate the control design algorithm.