Generalized Results for Stability Analysis of Time-Varying Delay Systems via Necessary and Sufficient Conditions on High-Order Polynomial Inequality

This manuscript suggests generalized stability results of time-varying delay systems by utilizing a sufficient and necessary condition on the high-order polynomial inequality and a generalized integral inequality. Firstly, the Lyapunov-Krasovskii functionals are established in a generalized form to the bounding order. Secondly, the upper bound of a single integral in quadratic matrix form stacked with two state information is estimated through the generalized integral inequality which can provide an estimate generalized in the bounding order. Finally, the negative-definiteness conditions on a high-order matrix-valued polynomial, obtained from the stability analysis results, are converted to the linear matrix inequality conditions by applying the lemma of necessary and sufficient conditions on high-order polynomial inequality. Two numerical examples clearly show that the generalized stability results outperform the stability results of other conventional papers.