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Machine-learning technologies for learning dynamical systems from data playan important role in engineering design. This research focuses on learningcontinuous linear models from data. Stability, a key feature of dynamicsystems, is especially important in design tasks such as prediction andcontrol. Thus, there is a need to develop methodologies that provide stabilityguarantees. To that end, we leverage the parameterization of stable matricesproposed in [Gillis/Sharma, Automatica, 2017] to realize the desired models.Furthermore, to avoid the estimation of derivative information to learncontinuous systems, we formulate the inference problem in an integral form. Wealso discuss a few extensions, including those related to control systems.Numerical experiments show that the combination of a stable matrixparameterization and an integral form of differential equations allows us tolearn stable systems without requiring derivative information, which can bechallenging to obtain in situations with noisy or limited data.

Inference of Continuous Linear Systems from Data with Guaranteed Stability