A Hierarchical Stability Criterion for Time-Delay Systems based on the Affine Bessel-Legendre Inequality

초록

Recently, the affine Bessel-Legendre(BL) inequality has been presented for a stability analysis of linear systems with time-varying delays. If the degree of the inequality increases, much less conservative stability conditions can be derived but an appropriate design of Lyapunov-Krasovskii functionals and its treatment should be followed. This paper proposes a hierarchical stability criterion of time-delay systems along with the degree of the affine BL inequality based on a novel generalized Lyapunov-Krasovskii functional. With the help of the proposed approach, the stability criteria for various degrees of the inequality can easily be obtained. A numerical example shows the generality and the efficiency of the proposed approach.

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