  In this paper, we propose an LMI-based approach to analyze input-output
properties of coupled linear PDE systems. This work expands on a newly
developed state-space theory for coupled PDEs and extends the positive-real and
bounded-real lemmas to infinite dimensional systems. We show that conditions
for passivity and bounded L2 gain can be expressed as linear operator
inequalities on RxL2. A method to convert these operator inequalities to LMIs
by using parameterization of the operator variables is proposed. This method
does not rely on discretization and as such, the properties obtained are prima
facie provable. We use numerical examples to demonstrate that the bounds
obtained are not conservative in any significant sense and that the bounds are
computable on desktop computers for systems consisting of up to 20 coupled
PDEs.
