A generalized passivity theory over abstract time domains
File(s)
Author(s)
Moreschini, Alessio
Bin, Michelangelo
Astolfi, Alessandro
Parisini, Thomas
Type
Journal Article
Abstract
Passivity is a well-established concept for continuous-time systems. Yet, its application to discrete time, delay, or other classes of systems is somewhat limited, leading to inconsistencies and disparities. In this article, we study a new notion, ϱ-passivity, which reduces to standard passivity in the continuous-time case but addresses some of the aforementioned limitations when applied to other classes of systems. In particular, in an abstract input–output setting, we show that ϱ-passivity is preserved under a class of interconnections, thereby extending the existing passivity results. Moreover, we explore the relationship between ϱ-passivity and stability, and we derive sufficient conditions for high-gain, low-gain, and causal stabilizability by static output feedback. Finally, in contrast to the standard passivity notion, we prove that ϱ-passivity is preserved under sampling for a class of nonlinear systems and discretization methods. Overall, the results of this article constitute the first step toward a unifying passivity theory embracing all the different domains and systems classes relevant to systems and control theory.
Date Issued
2025-01-01
Date Acceptance
2024-06-22
Citation
IEEE Transactions on Automatic Control, 2025, 70 (1), pp.2-17
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
2
End Page
17
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
70
Issue
1
Copyright Statement
© 2024 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/
License URL
Subjects
Automation & Control Systems
DISSIPATIVE DYNAMICAL-SYSTEMS
Engineering
Engineering, Electrical & Electronic
High-gain stabilization
INPUT-OUTPUT
input-output systems
INTERCONNECTION
low-gain stabilization
output-feedback stabilization
passivity
sampled-data systems
Science & Technology
SECANT CONDITION
STABILITY
STABILIZATION
Technology
Publication Status
Published
Date Publish Online
2024-07-04