Stability Analysis of Linear System with Time-Varying Delays via new Negative Conditions for a Quadratic Function

This paper is concerned with the stability analysis of linear system with time-varying delays. First, new conditions that ensure the quadratic function is negative in finite interval are proposed by dividing the time interval into
$N$
parts and taking full advantage of the convex and concave properties of the quadratic function in each part. Second, a new zero equality including the square terms of time-varying delays is proposed, which is helpful to obtain a less conservative stability criterion. Third, a less conservative stability criterion is proposed based on the new negative conditions and the new zero equality. Finally, a typical example is used to verify the advantages and effectiveness of our newly proposed methods in the stability analysis of linear system with time-varying delays.