Comparison of some bounding inequalities applied in stability analysis of time-delay systems

Abstract This paper gives comparisons of several bounding inequalities proposed recently for the estimation of integrals and sums of quadratic functions, which plays an important role in stability analysis of time delay systems via the Lyapunov–Krasovskii approach. The equivalences of several known variants of the free matrix based inequalities and their generalized and simplified forms are shown. Secondly, the relationship between the (simplified) free matrix based inequality and the combination of the Bessel-based inequality with different bounding inequalities affine in the length of the intervals are investigated. Finally, we shall demonstrate the theoretical results with the application of the various estimations for the stability analysis of a linear system with time-varying delay using the same Lyapunov–Krasovskii functional.

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