Abstract
Consider the linear dynamic equation on time scales (1) where , , is a rd-continuous function, T is a time scales. In this paper, we shall investigate some results for the exponential stability of the dynamic Equation (1) by combinating the first approximate method and the second method of Lyapunov.
Highlights
Let Rn be a n-dimension Euclidean space, T be a time scales
We shall use the notions which appear in the book by Bohner and Peterson
The notions related to the Lyapunov function that we use follow the results of B
Summary
Let Rn be a n-dimension Euclidean space, T be a time scales (a nonempty closed subset of R). (2014) Combining Methods of Lyapunov for Exponential Stability of Linear Dynamic Systems on Time Scales. 0. We suppose that F satisfies all conditions such that (2) has this paper, we define the stable notions of the trivial solution a x unique (t) = 0 of (2) as the followings: Definition 1. The content of this paper contains two parts: the first part presents the sufficient conditions following the first approximate method for the exponential stability of the solution of the linear dynamic Equation (1) on time scales. This theorem can be seen as a corollary of the stable criterion which was presented in [3]
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