  In this paper, we present an algorithm for stability analysis of systems
described by coupled linear Partial Differential Equations (PDEs) with constant
coefficients and mixed boundary conditions. Our approach uses positive matrices
to parameterize functionals which are positive or negative on certain function
spaces. Applying this parameterization to construct Lyapunov functionals with
negative derivative allows us to express stability conditions as a set of LMI
constraints which can be constructed using SOSTOOLS and tested using standard
SDP solvers such as SeDuMi. The results are tested using a simple numerical
example and compared results obtained from simulation using a standard form of
discretization.
