TY - GEN
T1 - A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
AU - Shivakumar, Sachin
AU - Das, Amritam
AU - Weiland, Siep
AU - Peet, Matthew M.
N1 - Funding Information:
This work was supported by Office of Naval Research Award N00014-17-1-2117 and National Science Foundation under grant No. 1739990.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - In 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 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 a positive matrix parameterization of bounded operators resulting in a finite-dimensional LMI, the feasibility of which implies prima facie provable passivity or Lgain of the system. No discretization or approximation is involved at any step and there is no conservatism in the theorems. Comparison with other computational methods show that bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.
AB - In 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 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 a positive matrix parameterization of bounded operators resulting in a finite-dimensional LMI, the feasibility of which implies prima facie provable passivity or Lgain of the system. No discretization or approximation is involved at any step and there is no conservatism in the theorems. Comparison with other computational methods show that bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.
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U2 - 10.1109/CDC40024.2019.9030224
DO - 10.1109/CDC40024.2019.9030224
M3 - Conference contribution
AN - SCOPUS:85082482686
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 280
EP - 285
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
Y2 - 11 December 2019 through 13 December 2019
ER -