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.
Highlights
In natural systems engineering, the lowest level in the hierarchical structure is usually characterized by the dynamics of a continuous variable while the highest level is described by a logical decision making mechanism [8]
From a modeling point of view, it is perhaps more realistic to model a phenomenon by a dynamic system, which incorporates both discrete and continuous times simultaneously, namely by considering time as an arbitrary closed set of reals, called a time scale
We propose a new approach to investigate practical stability of hybrid fuzzy systems on time scales
Summary
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 show the validity of the results of M. Sambandham: Hybrid fuzzy systems on time scales, Dynam. Systems Appl., 12 (1–2) (2003), 217–227, by embedding the space of all fuzzy subsets into a suitable Banach space
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