Novel inequality-based functions for the stability of time-varying delay systems

This paper proposes new inequality-based functions to be Lyapunov functionals for the stability analysis of time-varying delay systems. The novel Lyapunov functionals are developed using a slack-matrices-based integral inequality for the first time. This is unlike most inequality-based functions that have been used as Lyapunov functionals which consist of single-matrices in their integral terms. Based on the new Lyapunov functionals, a new stability criterion is derived in the form of a matrix-valued quadratic function, which is proven to be negative definite using a geometry-based negativeness lemma. Two numerical examples showcase the effectiveness of our presented method.