Discrete-time convergent nonlinear systems
File(s)
Accepted version
Author(s)
Jungers, Marc
Shakib, Mohammad Fahim
van de Wouw, Nathan
Type
Journal Article
Abstract
The convergence property of discrete-time nonlinear systems is studied in this article. The main result provides a Lyapunov-like characterization of the convergence property based on two distinct Lyapunov-like functions. These two functions are associated with the incremental stability property and the existence of a compact positively invariant set, which together guarantee the existence of a well-defined, bounded, and unique steady-state solution. The links with the conditions available in recent literature are discussed. These generic results are subsequently used to derive constructive conditions for the class of discrete-time Lur'e-type systems. Such systems consist of an interconnection between a linear system and a static nonlinearity that satisfies cone-bounded (incremental) sector conditions. In this framework, the Lyapunov-like functions that characterize convergence are determined by solving a set of linear matrix inequalities. Several classes of Lyapunov-like functions are considered: both Lyapunov–Lur'e-type functions and quadratic functions. A numerical example illustrates the applicability of the results.
Date Issued
2024-10-01
Date Acceptance
2024-03-09
Citation
IEEE Transactions on Automatic Control, 2024, 69 (10), pp.6731-6745
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
6731
End Page
6745
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
69
Issue
10
Copyright Statement
Copyright © 2024 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Subjects
Asymptotic stability
Automation & Control Systems
CONTRACTION ANALYSIS
Convergence
Convergent systems
discrete-time Lyapunov Lur'e functions
discrete-time systems
Engineering
Engineering, Electrical & Electronic
INVERSION
linear matrix inequalities (LMIs)
LURE
Lur'e systems
LYAPUNOV FUNCTIONS
Lyapunov methods
Nonlinear systems
Science & Technology
stability analysis
STABILITY ANALYSIS
Stability criteria
Steady-state
Symmetric matrices
Technology
Publication Status
Published
Date Publish Online
2024-03-25