Determining the Viability of an Unbounded Polyhedron for a Switched System
This paper proposes a new method to determine the viability of a switched system on a cone and an unbounded polyhedron. First, we investigate the viability condition on a cone. Then, a sufficient viability criterion for a polyhedron, which is expressed by a convex hull of finite number of extreme po...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/1153483 |
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| _version_ | 1832547375402450944 |
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| author | Jianfeng Lv Na Zhao |
| author_facet | Jianfeng Lv Na Zhao |
| author_sort | Jianfeng Lv |
| collection | DOAJ |
| description | This paper proposes a new method to determine the viability of a switched system on a cone and an unbounded polyhedron. First, we investigate the viability condition on a cone. Then, a sufficient viability criterion for a polyhedron, which is expressed by a convex hull of finite number of extreme points and a nonnegative linear combination of finite extreme directions, is presented by using nonsmooth analysis. Based on this criterion, instead of all boundary points, just several extreme points and extreme directions are needed to be verified whether satisfying some conditions. The advantage of the proposed methods is that determining the viability for a switched system is easy to be implemented. Finally, an example is listed to illustrate the effectiveness of the proposed methods. |
| format | Article |
| id | doaj-art-92f5efab5f10409e9a380490c08ac0cd |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-92f5efab5f10409e9a380490c08ac0cd2025-02-03T06:45:11ZengWileyDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/1153483Determining the Viability of an Unbounded Polyhedron for a Switched SystemJianfeng Lv0Na Zhao1School of ScienceSchool of ScienceThis paper proposes a new method to determine the viability of a switched system on a cone and an unbounded polyhedron. First, we investigate the viability condition on a cone. Then, a sufficient viability criterion for a polyhedron, which is expressed by a convex hull of finite number of extreme points and a nonnegative linear combination of finite extreme directions, is presented by using nonsmooth analysis. Based on this criterion, instead of all boundary points, just several extreme points and extreme directions are needed to be verified whether satisfying some conditions. The advantage of the proposed methods is that determining the viability for a switched system is easy to be implemented. Finally, an example is listed to illustrate the effectiveness of the proposed methods.http://dx.doi.org/10.1155/2023/1153483 |
| spellingShingle | Jianfeng Lv Na Zhao Determining the Viability of an Unbounded Polyhedron for a Switched System Discrete Dynamics in Nature and Society |
| title | Determining the Viability of an Unbounded Polyhedron for a Switched System |
| title_full | Determining the Viability of an Unbounded Polyhedron for a Switched System |
| title_fullStr | Determining the Viability of an Unbounded Polyhedron for a Switched System |
| title_full_unstemmed | Determining the Viability of an Unbounded Polyhedron for a Switched System |
| title_short | Determining the Viability of an Unbounded Polyhedron for a Switched System |
| title_sort | determining the viability of an unbounded polyhedron for a switched system |
| url | http://dx.doi.org/10.1155/2023/1153483 |
| work_keys_str_mv | AT jianfenglv determiningtheviabilityofanunboundedpolyhedronforaswitchedsystem AT nazhao determiningtheviabilityofanunboundedpolyhedronforaswitchedsystem |