Abstract
This paper presents a computational framework for analyzing stability and performance of uncertain Partial Differential Equations (PDEs) when they are coupled with uncertain Ordinary Differential Equations (ODEs). To analyze the behavior of the interconnected ODE-PDE systems under uncertainty, we introduce a class of multipliers of Partial Integral (PI) operator type and consider various classes of uncertainties by enforcing constraints on these multipliers. Since the ODE-PDE models are equivalent to Partial Integral Equations (PIEs), we show that the robust stability and performance can be formulated as Linear PI Inequalities (LPIs) and LPIs can be solved by LMIs using PIETOOLS. The methods are demonstrated on examples of ODE-PDE systems that are subjected to wide classes of uncertainty.
Original language | English |
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Title of host publication | 2020 59th IEEE Conference on Decision and Control, CDC 2020 |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 634-639 |
Number of pages | 6 |
ISBN (Electronic) | 978-1-7281-7447-1 |
DOIs | |
Publication status | Published - 14 Dec 2020 |
Event | 59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020 |
Conference
Conference | 59th IEEE Conference on Decision and Control, CDC 2020 |
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Country | Korea, Republic of |
City | Virtual, Jeju Island |
Period | 14/12/20 → 18/12/20 |