Dissipative delay range analysis of coupled differential-difference delay systems with distributed delays

TL;DR

This paper develops new Lyapunov-Krasovskii functionals and LMI-based methods for analyzing the delay stability range of coupled differential-difference systems with distributed delays under dissipative constraints, applicable to delay margin estimation.

Contribution

It introduces a novel Lyapunov-Krasovskii functional with non-constant matrix parameters and a sum of squares programming approach to derive less conservative stability conditions for CDDS.

Findings

Effective stability range analysis for CDDS with distributed delays.

LMI conditions guarantee delay stability under dissipative constraints.

Numerical examples confirm the method's accuracy and applicability.

Abstract

This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains many models of linear delay systems as special cases. A novel Liapunov-Krasovskii functional with non-constant matrix parameters, which are related to the delay value polynomially, is applied to derive stability conditions. By constructing this new functional, sufficient conditions in terms of robust linear matrix inequalities (LMIs) can be derived, which guarantee range stability of a linear CDDS subject to dissipative constraints. To solve the resulting robust LMIs numerically, we apply the technique of sum of squares programming together with matrix relaxations without introducing any potential conservatism to the original robust LMIs. Furthermore, the proposed methods can be extended to solve delay margin estimation problems for a linear CDDS subject to prescribed dissipative constraints. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.