Solving Infinite-Dimensional Harmonic Lyapunov and Riccati Equations

• 成果类型: Article
• 署名作者: Riedinger, Pierre; Daafouz, Jamal
• 署名单位: Universite de Lorraine
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3229943
• 发表日期: 2023
• 页码: 5938-5953
• 关键词: Dynamic phasors; floquet factorization; harmonic Lyapunov equations; harmonic Riccati equations; harmonic modeling and control; periodic systems; sliding fourier decomposition

摘要

In this article, we address the problem of solving infinite-dimensional harmonic algebraic Lyapunov and Riccati equations up to an arbitrary small error. This question is of major practical importance for analysis and stabilization of periodic systems including tracking of periodic trajectories. We first give a closed form of a Floquet factorization in the general setting of L-2 matrix functions and study the spectral properties of infinite-dimensional harmonic matrices and their truncated version. This spectral study allows us to propose a generic and numerically efficient algorithm to solve infinite-dimensional harmonic algebraic Lyapunov equations up to an arbitrary small error. We combine this algorithm with the Kleinman algorithm to solve infinite-dimensional harmonic Riccati equations and we apply the proposed results to the design of a harmonic LQ control with periodic trajectory tracking.