Two-sided dimension reduction for linear control systems of kth-order form

• Published in: European journal of control Vol. 69
• Main Authors: Yang, Jun-Man, Jiang, Yao-Lin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2023
• Subjects: [formula omitted]th-order control systems; [formula omitted]th-order Krylov subspace; Petrov–Galerkin framework; Recurrence form of moments; Two-sided dimension reduction; kth-order Krylov subspace; kth-order control systems; Two-sided dimension reduction; Recurrence form of moments; Petrov–Galerkin framework
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2022.100722

•The number of moments matched is twice as much as the order of the reduced system when we take two-sided dimension reduction method.•The method is structure-preserving.•Prove it is necessary to consider the moment matching at the nonzero frequency point via numerical experiments. In this article, a two-sided structure-preserving dimension reduction method for linear control systems of kth-order form is discussed. We first recall the Petrov–Galerkin framework of dimension reduction for the kth linear systems. Then the moments of systems at a given frequency point s0 are discussed. According to the recurrence form of the moments, we obtain the input Krylov subspace and the projection matrix V. Via dually designing output Krylov subspace, we obtain the output Krylov subspace basis matrix W. Hence, the two-sided dimension reduction method is obtained via combination V with W. Afterwards one can obtain the result that the number of moments matched is twice as much as the column dimension of the projection matrix. Finally, one numerical experiment is performed to verify the proposed dimension reduction method.