Stability of distributed delay systems via a robust approach

Abstract

This paper is dedicated to the stability analysis of a class of distributed delay systems with a non constant kernel. By the use of appropriate orthogonal polynomials, this kernel is expressed as the sum of a polynomial and an additive bounded function. The resulting system is then modeled by an interconnected system between a nominal finite dimensional linear system and a infinite dimensional system. This last system is considered as a structured uncertainty and embedded into some well defined structured uncertainties. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. Finally, numerical examples show the effectiveness of the proposed method.

Dissipative stabilization of linear systems with time-varying general distributed delays

“…Although the method in Ngoc (2013) does include criteria to determine the stability of non-positive linear systems, the structure of the delay function r(•) ∈ [0, r 2 ] R therein is still restrictive. On the other hand, the synthesis (stability analysis) methods proposed in Münz et al (2009); Goebel et al (2011); Gouaisbaut et al (2015); Seuret et al (2015); Feng & Nguang (2016), which are developed to handle linear distributed delay systems with constant delay values, may not be easily extended to cope with systems with an unknown time-varying delay r(•) ∈ [r 1 , r 2 ] R . This is especially true for the approximation approaches established in Münz et al (2009); Goebel et al (2011); Gouaisbaut et al (2015); Seuret et al (2015), since the approximation coefficients can become nonlinear with respect to r(t) if the distributed delay kernels are approximated over [−r(t), 0].…”

Stability of Distributed Delay System with Infinite Support

“…Concerning distributed time-delay systems with a finite support, several papers have been devoted to the construction of Lyapunov functionals [3], [4], [5] (and references therein). The methodology involving orthogonal Legendre polynomials has also led to results reducing the conservatism of Lyapunov methods and keeping a relatively low numerical complexity [17], [6].…”