An Affine Integral Inequality of an Arbitrary Degree for Stability Analysis of Linear Systems With Time-Varying Delays

This paper is concerned with the stability analysis problems of linear systems time-varying delays using integral inequalities. To reduce conservatism criteria obtained Lyapunov-Kraosvksii approach, there has been a growing tendency to utilize various quadratic functions in construction Lyapunov-Krasovskii functionals. Consequently, inequalities also have played key roles derive guaranteeing negativity functional’s derivative. Recently, by utilizing first-degree or second-degree orthogonal polynomials, new free-matrix-based proposed for containing both system state variable and its time tries generalize these their note on relation among existing one. In this note, it shown that increasing degree inequality only reduces maintains deriving hierarchical criteria. Four numerical examples including practical demonstrate effectiveness methods terms allowable upper delay bounds.