Some Theorems of Uncertain Multiple-Delay Differential Equations
Uncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differential equations with multiple delays. This paper defin...
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2024-11-01
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| author | Yin Gao Han Tang |
| author_facet | Yin Gao Han Tang |
| author_sort | Yin Gao |
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| description | Uncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differential equations with multiple delays. This paper defines uncertain differential equations with multiple delays, which are called uncertain multiple-delay differential equations (UMDDEs). Based on the linear growth condition and the Lipschitz condition, the existence and uniqueness theorem of the solutions to the UMDDEs is proven. In order to judge the stability of the solutions to the UMDDEs, the concept of the stability in measure for UMDDEs is presented. Moreover, two theorems sufficient for use as tools to identify the stability in measure for UMDDEs are proved, and some examples are also discussed in this paper. |
| format | Article |
| id | doaj-art-225792d089c04a16b82b9ef29f7132b3 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
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| series | Axioms |
| spelling | doaj-art-225792d089c04a16b82b9ef29f7132b32024-11-26T17:50:57ZengMDPI AGAxioms2075-16802024-11-01131179710.3390/axioms13110797Some Theorems of Uncertain Multiple-Delay Differential EquationsYin Gao0Han Tang1College of Science, Beijing Forestry University, Beijing 100872, ChinaDepartment of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaUncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differential equations with multiple delays. This paper defines uncertain differential equations with multiple delays, which are called uncertain multiple-delay differential equations (UMDDEs). Based on the linear growth condition and the Lipschitz condition, the existence and uniqueness theorem of the solutions to the UMDDEs is proven. In order to judge the stability of the solutions to the UMDDEs, the concept of the stability in measure for UMDDEs is presented. Moreover, two theorems sufficient for use as tools to identify the stability in measure for UMDDEs are proved, and some examples are also discussed in this paper.https://www.mdpi.com/2075-1680/13/11/797existence and uniqueness theoremstability in measureuncertain multiple-delay differential equationsuncertain theory |
| spellingShingle | Yin Gao Han Tang Some Theorems of Uncertain Multiple-Delay Differential Equations Axioms existence and uniqueness theorem stability in measure uncertain multiple-delay differential equations uncertain theory |
| title | Some Theorems of Uncertain Multiple-Delay Differential Equations |
| title_full | Some Theorems of Uncertain Multiple-Delay Differential Equations |
| title_fullStr | Some Theorems of Uncertain Multiple-Delay Differential Equations |
| title_full_unstemmed | Some Theorems of Uncertain Multiple-Delay Differential Equations |
| title_short | Some Theorems of Uncertain Multiple-Delay Differential Equations |
| title_sort | some theorems of uncertain multiple delay differential equations |
| topic | existence and uniqueness theorem stability in measure uncertain multiple-delay differential equations uncertain theory |
| url | https://www.mdpi.com/2075-1680/13/11/797 |
| work_keys_str_mv | AT yingao sometheoremsofuncertainmultipledelaydifferentialequations AT hantang sometheoremsofuncertainmultipledelaydifferentialequations |