Before revision:  The Koopman representation of the nonlinear system is then used to synthesize LQRfeedback .
After revision:  Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system is then used to synthesize LQRfeedback .