Some applications of passivity-based control and invariance principles

• Published in: IET control theory & applications 2013-05, Vol.7 (7), p.1039-1048
• Main Author: de Ruiter, Anton H. J
• Format: Article
• Language: English
• Subjects: actuator saturation constraint; actuators; asymptotic convergence; Asymptotic properties; asymptotic stability; closed loop systems; closed‐loop global stability; closed‐loop system; Control theory; Convergence; feedback; Feedback control; feedback control law; Invariance; invariance principle; Law; passive feedback; passive plant; passivity theorem; passivity‐based control; Representations; Stability; state representation
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2012.0691

This study examines the control of a passive plant utilising strictly passive feedback as motivated by the passivity theorem. A state representation of the plant is assumed with very few conditions imposed. No assumptions are made on the state representation of the feedback control law. However, some mild additional input–output properties of the feedback control law are assumed. Global stability of the closed-loop system and asymptotic convergence of a subset of the states is proven using invariance principles. The theoretical results in the study are applied to a number of application examples, demonstrating that a much broader class of controllers can deliver closed-loop global stability and asymptotic convergence, unlike the previous works in the literature where the examples are taken from. In one of the examples, it is demonstrated that actuator saturation constraints can readily be handled using the theory presented in this study.