Dissipative analysis of linear coupled differential-difference systems with distributed delays

TL;DR

This paper introduces a new method for analyzing the stability and dissipativity of linear coupled differential-difference systems with distributed delays, using a broader class of delay functions and a novel integral inequality.

Contribution

It develops a generalized approach with non-polynomial function approximation and a new integral inequality for stability analysis of CDDS with distributed delays.

Findings

Effective stability conditions derived as linear matrix inequalities.

Broader class of delay functions including non-polynomial functions.

Numerical examples demonstrate the method's effectiveness.

Abstract

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay terms under consideration can contain any $\fL^{2}$ functions which are approximated via a class of elementary functions which includes the option of Legendre polynomials. By using this broader class of functions compared to the existing Legendre polynomials approximation approach, one can construct a Liapunov-Krasovskii functional which is parameterized by non-polynomial functions . Furthermore, a novel generalized integral inequality is also proposed to incorporate approximation error in our stability (dissipativity) conditions. Based on the proposed approximation scenario with the proposed integral inequality, sufficient conditions determining the dissipativity and stability of a CDDS are derived in terms of linear matrix inequalities. In addition, several hierarchies in terms of the feasibility of the proposed conditions are derived under certain constraints. Finally, several numerical examples are presented in this paper to show the effectiveness of our proposed methodologies.