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The complexity of human-machine interaction (HMI) is rapidly growing in modern industrial, medical, and military systems. Human operators are often challenged by control of high-order systems or unstable systems near the limits of controllability. However, there is no quantitative indication of human performance and cognitive workload in these difficult HMI tasks. Here, we characterize HMI as information flows measured in bits per second (b/s). We propose a control-theoretic framework to estimate the rate of information transmission in manual control. We demonstrate our method in an example of stabilizing an inverted pendulum, where we derive that, for a normal human operator, the information-transmission rate of manual control with one degree of freedom ranges between 3 and 4 b/s. This quantitative indication reveals the potential and limitation of human manual control and is instructive to the design of HMI interfaces that may maximally utilize human control commands.