2022/03/18 by Pierre Riedinger, Riedinger, Pierre, Jamal Daafouz +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical methods for differential equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2203.09774
openalex publication_date 2022/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, 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.