  We present a dual form of Lyapunov-Krasovskii functional which allows the
problem of controller synthesis of multi-delay systems to be formulated and
solved in a convex manner. First, we give a general form of dual stability
condition formulated in terms of Lyapunov operators which are positive,
self-adjoint and preserve the structure of the state-space. Second, we provide
a class of such operators and express the stability conditions as positivity
and negativity of quadratic Lyapunov-Krasovskii functional forms. Next, we
adapt the SOS methodology to express positivity and negativity of these forms
as LMIs, describing a new set of polynomial manipulation tools designed for
this purpose. Finally, we apply the resulting LMIs to a battery of numerical
examples and demonstrate that the stability conditions are not conservative.
The results of this paper are significant in that they open the way for dynamic
output H-infinity optimal control of systems with multiple time-delays.
