Lyapunov-like functions for almost global convergence in discrete-time systems

Mohammadreza Kamaldar; Jesse B. Hoagg

doi:10.1016/j.sysconle.2024.105807

Lyapunov-like functions for almost global convergence in discrete-time systems

Mohammadreza Kamaldar
, Jesse B. Hoagg

Mechanical and Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents new results on discrete-time almost global convergence to an invariant set. First, we present new sufficient conditions for almost global convergence using density functions. In contrast to existing density-function results, the new results in this paper do not rely on a local convergence assumption, and they do not require knowledge of the inverse map of the difference equation. Next, we present new sufficient conditions for almost global convergence using Lyapunov-like functions rather than density functions. These Lyapunov-like results can be useful because constructing and analyzing density functions is often difficult in comparison to Lyapunov-like analysis. This paper also presents a variety of simple examples to illustrate these new methods for almost global convergence analysis.

Original language	English
Article number	105807
Journal	Systems and Control Letters
Volume	188
DOIs	https://doi.org/10.1016/j.sysconle.2024.105807
State	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Funding

This work is supported in part by the Air Force Office of Scientific Research, United States (FA9550-20-1-0028).This work is supported in part by the Air Force Office of Scientific Research (FA9550-20-1-0028). The authors would also like to acknowledge the reviewers for their insightful feedback and for pointing out an issue in the original manuscript. The reviewers\u2019 feedback helped improve this paper.

Funders	Funder number
Air Force Office of Scientific Research, United States Air Force	FA9550-20-1-0028

Keywords

Almost global convergence
Density functions
Discrete time
Lyapunov-like functions

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/j.sysconle.2024.105807

Cite this

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title = "Lyapunov-like functions for almost global convergence in discrete-time systems",

abstract = "This paper presents new results on discrete-time almost global convergence to an invariant set. First, we present new sufficient conditions for almost global convergence using density functions. In contrast to existing density-function results, the new results in this paper do not rely on a local convergence assumption, and they do not require knowledge of the inverse map of the difference equation. Next, we present new sufficient conditions for almost global convergence using Lyapunov-like functions rather than density functions. These Lyapunov-like results can be useful because constructing and analyzing density functions is often difficult in comparison to Lyapunov-like analysis. This paper also presents a variety of simple examples to illustrate these new methods for almost global convergence analysis.",

keywords = "Almost global convergence, Density functions, Discrete time, Lyapunov-like functions",

author = "Mohammadreza Kamaldar and Hoagg, \{Jesse B.\}",

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year = "2024",

month = jun,

doi = "10.1016/j.sysconle.2024.105807",

language = "English",

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AU - Kamaldar, Mohammadreza

AU - Hoagg, Jesse B.

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N2 - This paper presents new results on discrete-time almost global convergence to an invariant set. First, we present new sufficient conditions for almost global convergence using density functions. In contrast to existing density-function results, the new results in this paper do not rely on a local convergence assumption, and they do not require knowledge of the inverse map of the difference equation. Next, we present new sufficient conditions for almost global convergence using Lyapunov-like functions rather than density functions. These Lyapunov-like results can be useful because constructing and analyzing density functions is often difficult in comparison to Lyapunov-like analysis. This paper also presents a variety of simple examples to illustrate these new methods for almost global convergence analysis.

AB - This paper presents new results on discrete-time almost global convergence to an invariant set. First, we present new sufficient conditions for almost global convergence using density functions. In contrast to existing density-function results, the new results in this paper do not rely on a local convergence assumption, and they do not require knowledge of the inverse map of the difference equation. Next, we present new sufficient conditions for almost global convergence using Lyapunov-like functions rather than density functions. These Lyapunov-like results can be useful because constructing and analyzing density functions is often difficult in comparison to Lyapunov-like analysis. This paper also presents a variety of simple examples to illustrate these new methods for almost global convergence analysis.

KW - Almost global convergence

KW - Density functions

KW - Discrete time

KW - Lyapunov-like functions

UR - https://www.scopus.com/pages/publications/85191294173

UR - https://www.scopus.com/pages/publications/85191294173#tab=citedBy

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DO - 10.1016/j.sysconle.2024.105807

M3 - Article

AN - SCOPUS:85191294173

SN - 0167-6911

VL - 188

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 105807

ER -

Lyapunov-like functions for almost global convergence in discrete-time systems

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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