Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality

Abstract

In this article, a new integral inequality based on a free-matrix for bounding the integral ∫abẋT(u)Rẋ(u)du has been proposed. The new inequality and appropriated Lyapunov–Krasovskii functional play key roles for deriving finite-time stability criteria of linear systems with constant and continuous non-differentiable time-varying delays. The new sufficient finite-time stability conditions have been proposed in the forms of inequalities and linear matrix inequalities. In addition, we apply the same procedure as done for deriving finite-time stable criteria but using Wirtinger-based inequality instead of our new inequality and compare these criteria with other works. At the end, two numerical examples are presented to show that the proposed criteria are practicable for linear systems with non-differentiable delay. Criteria using proposed integral inequality yield better results than the other works for linear system with constant delay. However, results using Wirtinger inequality are less conservative when time-varying delay is considered.