New summation inequalities and their applications to discrete-time delay systems

TL;DR

This paper introduces novel summation inequalities for discrete-time delay systems, enabling less conservative stability conditions and improving analysis accuracy through linear matrix inequalities.

Contribution

It presents new summation inequalities in single and double forms, enhancing stability analysis of discrete-time systems with time-varying delays.

Findings

Derived less conservative stability conditions

Validated effectiveness through academic examples

Demonstrated practical applicability

Abstract

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.