Representation and Stability Analysis of 1D PDEs with Periodic Boundary Conditions

arXiv:2503.22896 · math.AP, cs.SY, eess.SY, math.OC · Submitted 2025-03-28 · Read on arXiv

math.AP, cs.SY, eess.SY, math.OC

Submitted: 2025-03-28

Updated: 2025-09-02

Journal ref: Proceedings of the 64th IEEE Conference on Decision and Control, pp. 2050-2057, 2025

DOI: 10.1109/CDC57313.2025.11313012

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Partial Integral — 9× in this paper
• Partial Integral Equation — 5× in this paper
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Linear PI Inequality — 1× in this paper
• Lyapunov function — 1× in this paper · explained in 2 episodes

Sources

• Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations

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