Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval

- Journal title : The Transactions of The Korean Institute of Electrical Engineers
- Volume 65, Issue 3, 2016, pp.457-462
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/KIEE.2016.65.3.457

Title & Authors

Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval

Kim, Jin-Hoon;

Kim, Jin-Hoon;

Abstract

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen`s integral inequality was the best in the last two decades until Seuret`s integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret`s integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

Keywords

Stability;Time-delay;Proportional to integration interval;Integral inequality;LMI;

Language

Korean

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