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In this paper, we present a methodology for stability analysis of a generalclass of systems defined by coupled Partial Differential Equations (PDEs) withspatially dependent coefficients and a general class of boundary conditions.This class includes PDEs of the parabolic, elliptic and hyperbolic type as wellas coupled systems without boundary feedback. Our approach uses positivematrices to parameterize a new class of SOS Lyapunov functionals and combinesthese with a parametrization of projection operators which allow us to enforcepositivity and negativity on subspaces of L_2. The result allows us to expressLyapunov stability conditions as a set of Linear Matrix Inequality (LMI)constraints which can be constructed using SOSTOOLS and tested usingSemi-Definite Programming (SDP) solvers such as SeDuMi or Mosek. Themethodology is tested using several simple numerical examples and compared withresults obtained from simulation using a standard form of numericaldiscretization.

A Convex Approach for Stability Analysis of Coupled PDEs with Spatially Dependent Coefficients