A novel finite-sum inequality for stability of discrete-time linear systems with interval-like time-varying delays

This paper focuses on the stability analysis of a discrete-time linear system with an interval-like time-varying delay in the state. A novel inequality for finite-sum Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j=(r1)</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(r2)-1</sup> ω <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> (j)Rω(j) is first established, where r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> are integers or integer-valued functions and R is a symmetric definite positive matrix. One of advantages of this inequality is that the factor r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> appears in the estimation of the finite-sum linearly. The new inequality together with convex combination technique results in a novel delay-dependent stability criterion, which has been proven theoretically to be less conservative than some existing ones reported in the literature. Two numerical examples are given to show the validity of the proposed method.