Molodchyk, OleksiiOleksiiMolodchykFaulwasser, TimmTimmFaulwasser2024-08-212024-08-212024-05-27IEEE Control Systems Letters 8: 2045 - 2050 (2024-05-27)https://hdl.handle.net/11420/48813Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.en2475-1456202420452050Institute of Electrical and Electronics Engineers Inc.data-driven controlkernel regressionreproducing kernel Hilbert spaceSystem identificationComputer Science, Information and General Works::005: Computer Programming, Programs, Data and SecurityNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Article10.1109/LCSYS.2024.3406053Journal Article