A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP

arXiv:2508.14840 · math.AP, cs.SY, eess.SY · Submitted 2025-08-20 · Read on arXiv

math.AP, cs.SY, eess.SY

Submitted: 2025-08-20

Updated: 2026-09-16

Terminology

• Consistency — 23× in this paper · explained in 3 episodes
• Partial Integral — 11× in this paper
• Hilbert Space — 8× in this paper · explained in 2 episodes
• Partial Integral Equation — 7× in this paper
• Accuracy — 6× in this paper · explained in 1 episode
• Admissibility — 4× in this paper · explained in 2 episodes
• alpha — 3× in this paper · explained in 1 episode
• Trace — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Sharpness and non-sharpness of occupation measure bounds for integral variational problems
• Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations
• Verifying Well-Posedness of Linear PDEs using Convex Optimization
• Backstepping for Partial Differential Equations:A Survey
• Late lumping of transformation-based feedback laws for boundary control systems
• Extension of the Partial Integral Equation Representation to GPDE Input-Output Systems

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