  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.
