A Hukuhara approach to the study of hybrid fuzzy systems on time scales

TL;DR

This paper presents a novel Lyapunov-based approach using delta-Hukuhara derivatives to analyze the stability of hybrid fuzzy systems on time scales, extending existing results through embedding fuzzy sets into Banach spaces.

Contribution

It introduces a new stability analysis method for hybrid fuzzy systems on time scales using delta-Hukuhara derivatives, expanding the theoretical framework.

Findings

Derived new stability criteria for hybrid fuzzy systems

Validated results by embedding fuzzy sets into Banach spaces

Extended previous stability results in the literature

Abstract

We introduce a new approach to study the practical stability of hybrid fuzzy systems on time scales in the Lyapunov sense. Our method is based on the delta-Hukuhara derivative for fuzzy valued functions and allow us to obtain new interesting stability criteria. We also show the validity of the results of [M. Sambandham: Hybrid fuzzy systems on time scales, Dynam. Systems Appl. 12 (2003), no. 1-2, 217-227], by embedding the space of all fuzzy subsets into a suitable Banach space.