Solutions of a Class of Switch Dynamical Systems
In this paper, the solutions of a class of switch dynamical systems are investigated. The right-hand side of the underlying equations is discontinuous with respect to the state variable. The discontinuity is represented by jump discontinuous functions such as signum or Heaviside functions. In this p...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/2/158 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850082431316525056 |
|---|---|
| author | Marius-F. Danca |
| author_facet | Marius-F. Danca |
| author_sort | Marius-F. Danca |
| collection | DOAJ |
| description | In this paper, the solutions of a class of switch dynamical systems are investigated. The right-hand side of the underlying equations is discontinuous with respect to the state variable. The discontinuity is represented by jump discontinuous functions such as signum or Heaviside functions. In this paper, a novel approach of the solutions of this class of discontinuous equations is presented. The initial value problem is restated as a differential inclusion via Filippov’s regularization, after which, via the approximate selection results, the differential inclusion is transformed into a continuous, single-valued differential equation. Besides its existence, a sufficient uniqueness condition, the strengthened one-sided Lipschitz Condition, is also introduced. The important issue of the numerical integration of this class of equations is addressed, emphasizing by examples the errors that could appear if the discontinuity problem is neglected. The example of a mechanical system, a preloaded compliance system, is considered along with other examples. |
| format | Article |
| id | doaj-art-c851cfbd71b64ca881e16a5da7e99fd1 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-c851cfbd71b64ca881e16a5da7e99fd12025-08-20T02:44:32ZengMDPI AGEntropy1099-43002025-02-0127215810.3390/e27020158Solutions of a Class of Switch Dynamical SystemsMarius-F. Danca0STAR-UBB Institute, Babes-Bolyai University, 400084 Cluj-Napoca, RomaniaIn this paper, the solutions of a class of switch dynamical systems are investigated. The right-hand side of the underlying equations is discontinuous with respect to the state variable. The discontinuity is represented by jump discontinuous functions such as signum or Heaviside functions. In this paper, a novel approach of the solutions of this class of discontinuous equations is presented. The initial value problem is restated as a differential inclusion via Filippov’s regularization, after which, via the approximate selection results, the differential inclusion is transformed into a continuous, single-valued differential equation. Besides its existence, a sufficient uniqueness condition, the strengthened one-sided Lipschitz Condition, is also introduced. The important issue of the numerical integration of this class of equations is addressed, emphasizing by examples the errors that could appear if the discontinuity problem is neglected. The example of a mechanical system, a preloaded compliance system, is considered along with other examples.https://www.mdpi.com/1099-4300/27/2/158Filippov regularizationone-sided Lipschitz conditionstrengthened one-sided Lipschitz conditiondifferential inclusionapproximate selection theorem |
| spellingShingle | Marius-F. Danca Solutions of a Class of Switch Dynamical Systems Entropy Filippov regularization one-sided Lipschitz condition strengthened one-sided Lipschitz condition differential inclusion approximate selection theorem |
| title | Solutions of a Class of Switch Dynamical Systems |
| title_full | Solutions of a Class of Switch Dynamical Systems |
| title_fullStr | Solutions of a Class of Switch Dynamical Systems |
| title_full_unstemmed | Solutions of a Class of Switch Dynamical Systems |
| title_short | Solutions of a Class of Switch Dynamical Systems |
| title_sort | solutions of a class of switch dynamical systems |
| topic | Filippov regularization one-sided Lipschitz condition strengthened one-sided Lipschitz condition differential inclusion approximate selection theorem |
| url | https://www.mdpi.com/1099-4300/27/2/158 |
| work_keys_str_mv | AT mariusfdanca solutionsofaclassofswitchdynamicalsystems |