Abstract
This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.
Highlights
In recent years, the investigation about the stability of timedelay systems has already become a nuclear problem with the emergence of both suitable theoretical tools and more complex practical issues in the engineering field and information technology such as ecology, economics, or biology
If some additional hypotheses are formulated on the Lyapunov functional, we can find that some conservative results are expressed in terms of LMIs
We resolve these problems by either choosing extended state based on Lyapunov-Krasovskii functional and/or discretized Lyapunov functional and/or improving the existing integral inequality
Summary
The investigation about the stability of timedelay systems has already become a nuclear problem with the emergence of both suitable theoretical tools and more complex practical issues in the engineering field and information technology such as ecology, economics, or biology (see [1,2,3,4,5,6]). This process exposes some limitations of itself that it cannot be spread straightway to other cases: the robust case and the system with time varying delay Another one is the use of Lyapunov-Krasovskii functionals. We resolve these problems by either choosing extended state based on Lyapunov-Krasovskii functional (see [19,20,21,22,23]) and/or discretized Lyapunov functional (see [6,7,8]) and/or improving the existing integral inequality (see [21, 22, 24,25,26]) Beyond that, another important technique reduces the conservatism, which is to bound some cross terms that have arisen when computing the derivative of Lyapunov functional.
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