Numerical design of Lyapunov functions for a class of homogeneous discontinuous systems

This paper deals with the analytical and numerical design of a Lyapunov function for homogeneous and discontinuous systems. First, the presented converse theorems provide two analytic expressions of homogeneous and locally Lipschitz continuous Lyapunov functions for homogeneous discontinuous systems...

Full description

Saved in:
Bibliographic Details
Published in:International journal of robust and nonlinear control 2021-06, Vol.31 (9), p.3708-3729
Main Authors: Mendoza‐Avila, Jesús, Efimov, Denis, Ushirobira, Rosane, Moreno, Jaime A.
Format: Article
Language:English
Subjects:
Algorithms
Automatic
Continuity (mathematics)
differential inclusions
discontinuous control
Engineering Sciences
Homogeneity
Liapunov functions
Lyapunov functions
nonlinear systems
Sliding mode control
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with the analytical and numerical design of a Lyapunov function for homogeneous and discontinuous systems. First, the presented converse theorems provide two analytic expressions of homogeneous and locally Lipschitz continuous Lyapunov functions for homogeneous discontinuous systems of negative homogeneity degree, generalizing classical results. Second, a methodology for the numerical construction of those Lyapunov functions is extended to the class of systems under consideration. Finally, the developed theory is applied to the numerical design of a Lyapunov function for some higher‐order sliding mode algorithms.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.5478