  This paper presents a data-driven method to identify an asymptotically stable
Koopman system from noisy data. In particular, the proposed approach combines
approximations of the system's forward- and backward-in-time dynamics to reduce
bias caused by noisy data while enforcing asymptotic stability. A Koopman model
of an inherently asymptotically stable system can be unstable due to noisy data
and a poor choice of lifting functions. To prevent identifying an unstable
model, the proposed approach imposes an asymptotic stability constraint on the
Koopman model. The proposed method is formulated as a semidefinite program and
its performance is compared to state-of-the-art methods with a simulated
Duffing oscillator dataset and experimental soft robot dataset.
