Work

Some Theorems of Uncertain Multiple-Delay Differential Equations

Year: 2024

Type: article

Abstract: 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.

Source: Axioms

DOI: 10.3390/axioms13110797

Authors: Yin Gao, Han Tang

Institutions: Beijing Forestry University, North China Electric Power University

Language: English

Topic: Fuzzy Systems and Optimization

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: Beijing Forestry University