A Chain Rule for Reduced Functional Differential Inclusions and Stability Theorems

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Black Sea Journal of Engineering and Science
Cilt: 8 Sayı: 5
A Chain Rule for Reduced Functional Differential Inclusions and Stability Theorems

A Chain Rule for Reduced Functional Differential Inclusions and Stability Theorems

Authors : Nurgul Gokgoz

Pages : 1556-1560

Doi:10.34248/bsengineering.1746300

View : 50 | Download : 46

Publication Date : 2025-09-15

Article Type : Research Paper

Abstract :In order to represent real-world problems, modeling and stability concepts of a system are two essential steps, and functional differential inclusions become favorable among other methods because of their flexibility and robustness to handle those problems. Thus, functional differential inclusions (FDIs) provide a solid foundation for engineering problems, and the calculation of their derivatives becomes an important issue in checking the stability of them. Especially, to check the Lyapunov stability, various chain rules for FDIs are defined in the literature. In this work, a new chain rule is introduced in terms of the reduction procedure, a comparison with another one is represented, and the stability theorems in terms of Lyapunov are extended to the reduced functional differential inclusions.
Keywords : Functional differential inclusions, Set-valued analysis, Convex analysis, Stability

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