TY - GEN
T1 - Computing input-ouput properties of coupled linear PDE systems
AU - Shivakumar, Sachin
AU - Peet, Matthew M.
N1 - Funding Information:
This work was supported by National Science Foundation under grants No. 1739990, 1538374 and by Office of Naval Research Award N00014-17-1-2117.
PY - 2019/7
Y1 - 2019/7
N2 - 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 R× L2. 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.
AB - 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 R× L2. 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.
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U2 - 10.23919/acc.2019.8814336
DO - 10.23919/acc.2019.8814336
M3 - Conference contribution
AN - SCOPUS:85072276660
T3 - Proceedings of the American Control Conference
SP - 606
EP - 613
BT - 2019 American Control Conference, ACC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 American Control Conference, ACC 2019
Y2 - 10 July 2019 through 12 July 2019
ER -