Stability and Lyapunov Theory
Karayiannidis, Yiannis LU
(2025)
p.98-109
- Abstract
- In this chapter, we explore mathematical tools for assessing the stability, convergence, and boundedness of trajectories in generally nonlinear dynamical systems. We delve into the seminal theorems introduced by A. Lyapunov which are primarily concerned with the stability of equilibrium points. The chapter progresses to discuss the extension of Lyapunov's Theory, due to LaSalle, aimed at assessing stability attributes of invariant sets, and the utilization of the Lyapunov equation, for investigating the stability of linear systems and systems amenable to linearization. Additionally, we extend stability analysis to systems with time-varying dynamics and how external disturbances influence the system's trajectory behavior through the concept... (More)
- In this chapter, we explore mathematical tools for assessing the stability, convergence, and boundedness of trajectories in generally nonlinear dynamical systems. We delve into the seminal theorems introduced by A. Lyapunov which are primarily concerned with the stability of equilibrium points. The chapter progresses to discuss the extension of Lyapunov's Theory, due to LaSalle, aimed at assessing stability attributes of invariant sets, and the utilization of the Lyapunov equation, for investigating the stability of linear systems and systems amenable to linearization. Additionally, we extend stability analysis to systems with time-varying dynamics and how external disturbances influence the system's trajectory behavior through the concept of Input-to-State Stability. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/99f02f8c-c7f1-491f-9e28-818e9ad877a7
- author
- Karayiannidis, Yiannis
LU
- organization
- publishing date
- 2025-09
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Asymptotic stability, Autonomous systems, Continuous-time differential equations, Control systems, Exponential stability, Input-to-state stability, Invariant and limits sets, Lyapunov theory, Nonlinear dynamical systems, Stability analysis, Uniform ultimate boundedness
- host publication
- Encyclopedia of Systems and Control Engineering (First Edition)
- editor
- Ding, Zhengtao
- edition
- First Edition
- pages
- 12 pages
- publisher
- Elsevier
- ISBN
- 978-0-443-14080-8
- DOI
- 10.1016/B978-0-443-14081-5.00057-X
- project
- Intelligent trajectory predictions at sea using neural ordinary differential equations
- language
- English
- LU publication?
- yes
- id
- 99f02f8c-c7f1-491f-9e28-818e9ad877a7
- alternative location
- https://www.sciencedirect.com/science/article/pii/B978044314081500057X
- date added to LUP
- 2025-09-19 18:56:08
- date last changed
- 2025-10-13 14:34:41
@inbook{99f02f8c-c7f1-491f-9e28-818e9ad877a7,
abstract = {{In this chapter, we explore mathematical tools for assessing the stability, convergence, and boundedness of trajectories in generally nonlinear dynamical systems. We delve into the seminal theorems introduced by A. Lyapunov which are primarily concerned with the stability of equilibrium points. The chapter progresses to discuss the extension of Lyapunov's Theory, due to LaSalle, aimed at assessing stability attributes of invariant sets, and the utilization of the Lyapunov equation, for investigating the stability of linear systems and systems amenable to linearization. Additionally, we extend stability analysis to systems with time-varying dynamics and how external disturbances influence the system's trajectory behavior through the concept of Input-to-State Stability.}},
author = {{Karayiannidis, Yiannis}},
booktitle = {{Encyclopedia of Systems and Control Engineering (First Edition)}},
editor = {{Ding, Zhengtao}},
isbn = {{978-0-443-14080-8}},
keywords = {{Asymptotic stability; Autonomous systems; Continuous-time differential equations; Control systems; Exponential stability; Input-to-state stability; Invariant and limits sets; Lyapunov theory; Nonlinear dynamical systems; Stability analysis; Uniform ultimate boundedness}},
language = {{eng}},
pages = {{98--109}},
publisher = {{Elsevier}},
title = {{Stability and Lyapunov Theory}},
url = {{http://dx.doi.org/10.1016/B978-0-443-14081-5.00057-X}},
doi = {{10.1016/B978-0-443-14081-5.00057-X}},
year = {{2025}},
}