Repetitive Control of Positive Real Systems via Delayed Feedback Is Lyapunov Asymptotically Stable

• Published in: IEEE transactions on automatic control Vol. 52; no. 9; pp. 1748 - 1751
• Main Author: Lucibello, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Asymptotic stability; Computer science; control theory; systems; Control systems; Control theory. Systems; Convergence; Delay; Delay systems; Differential equations; Exact sciences and technology; Feedback; linear systems; Lyapunov method; Lyapunov methods; Names; Repetitive control; Repetitive controllers; Robust stability; Stability; System theory; Topology; Trajectory; delay systems; Feedback regulation; Control systems; Delay system; linear systems; Topology; Positive system; Linear control; Periodic signal; Asymptotic stability; Linear system; Infinite dimension; Repetitive control; Lyapunov function; Lyapunov methods
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2007.904320

In this paper, we are concerned with the analysis of linear infinite-dimensional control systems that should be able to compensate and/or track signals that are periodic. Adopting the name given in the seminal paper by Hara et at, we call them repetitive controllers. We analyze the asymptotic stability in the Lyapunov sense of finite-dimensional positive real plants coupled with pure delays. For this class of systems, we initially prove convergence in the weak topology to later deduce convergence in the strong one.