Operator-Theoretic Stability and Observer Synthesis for Parameter-Dependent Vlasov--Maxwell Dynamics
Abstract
An operator--theoretic formulation is developed for the synthesis of parameter-dependent controllers and observers for the Vlasov--Maxwell system. The linearized dynamics are modeled as a non-autonomous evolution system whose generators depend on measurable plasma quantities. Well-posedness of the associated evolution family is established together with uniform growth bounds. Parameter-dependent Lyapunov operators yield operator differential LMIs ensuring uniform exponential stability and observer convergence. An H∞ extension provides disturbance attenuation conditions consistent with the intrinsic energy structure of the coupled Vlasov--Maxwell equations. Galerkin projections lead to finite-dimensional LMIs consistent with the operator inequalities, enabling reliable numerical synthesis while preserving the analytical structure of the original model. Numerical results on a reduced Vlasov--Maxwell benchmark confirm the predicted convergence properties.
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BibTeX
@misc{cisse2026operatortheoretic,
title = {{Operator-Theoretic Stability and Observer Synthesis for Parameter-Dependent Vlasov--Maxwell Dynamics}},
author = {Amadou Cissé and Mohamed Boutayeb},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28349},
eprint = {2608.28349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28349},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operator-Theoretic Stability and Observer Synthesis for Parameter-Dependent Vlasov--Maxwell Dynamics
AU - Amadou Cissé
AU - Mohamed Boutayeb
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28349
UR - https://arxiv.org/abs/2608.28349
AB - An operator--theoretic formulation is developed for the synthesis of parameter-dependent controllers and observers for the Vlasov--Maxwell system. The linearized dynamics are modeled as a non-autonomous evolution system whose generators depend on measurable plasma quantities. Well-posedness of the associated evolution family is established together with uniform growth bounds. Parameter-dependent Lyapunov operators yield operator differential LMIs ensuring uniform exponential stability and observer convergence. An H_∞ extension provides disturbance attenuation conditions consistent with the intrinsic energy structure of the coupled Vlasov--Maxwell equations. Galerkin projections lead to finite-dimensional LMIs consistent with the operator inequalities, enabling reliable numerical synthesis while preserving the analytical structure of the original model. Numerical results on a reduced Vlasov--Maxwell benchmark confirm the predicted convergence properties.
ER -