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Application of Double Integral Inequality for the Stability Analysis of the Singular Time-Varying Delay System

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This paper aims to establish and analyze the stability of continuous-time linear descriptor systems with a time-varying delay, based on the famous method Lyapunov KRASOVSKI function and the Linear Matrix Inequality (LMI) technique. The founded theorem, not only allows the stability, but also the admissibility, so that the regularity and the impulse free of the studied descriptor system.  The established criterion has been met using a neutral approach, which is the system transformation that checks singular time delayed system stability via a less complicated computation. Additionally to this new form, a major integral inequality lemma has also been used, due to its conservative results. The novelty of this idea is represented in the exploitation of the new double integral inequality proposed, in the admissibility analysis of singular time-delayed system via a neutral approach, which has been used to deliver an alternative delay dependent criterion in term of (LMI). The purpose of this idea is to check this admissibility of the said system through linear matrix inequality founded by programming it on the software numeric computing platform MATLAB. The originality of this article has been obtained by the combination of the double inequality technique and the neutral approach. At the end of this article, a numerical example has been provided using the LMI toolbox, in order to prove the validity and the efficiency of the proposed method. A comparison table will be presented to show the developed results in some other works compared with the proposed theorem, noting that the simulations of this example have been also performed in the MATLAB environment.
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Double Integral Inequality; Lyapunov Krasovski; Linear Matrix Inequality; Neutral Approach; Stability

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