%AShivakumar, S.%ADas, A.%AWeiland, S.%APeet, M.%BJournal Name: Proceedings of the IEEE Conference on Decision & Control
%D2020%I
%JJournal Name: Proceedings of the IEEE Conference on Decision & Control
%K
%MOSTI ID: 10113773
%PMedium: X
%TA Generalized LMI Formulation for Input-Output Analysis of Linear
Systems of ODEs Coupled with PDEs
%XIn this paper, we consider input-output properties
of linear systems consisting of PDEs on a finite domain coupled
with ODEs through the boundary conditions of the PDE. This
framework can be used to represent e.g. a lumped mass fixed
to a beam or a system with delay. This work generalizes the
sufficiency proof of the KYP Lemma for ODEs to coupled
ODE-PDE systems using a recently developed concept of
fundamental state and the associated boundary-condition-free
representation. The conditions of the generalized KYP are
tested using the PQRS positive matrix parameterization of
operators resulting in a finite-dimensional LMI, feasibility of
which implies prima facie provable passivity or L2-gain of
the system. No discretization or approximation is involved at
any step and we use numerical examples to demonstrate that
the bounds obtained are not conservative in any significant
sense and that computational complexity is lower than existing
methods involving finite-dimensional projection of PDEs.
%0Journal Article