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What qualifies a energy method in the context of control theory?

Citing from a paper to give the context in which this expression came to my attention:

One of the challenging problems of the double inverted pendulum is its swing-up from the downward position to the upright position. The swing-up of the double inverted pendulum can be performed by using an energy method and by separating the swing-up into three steps: first stabilizing the first pendulum in the upright position, then swinging-up the second pendulum while stabilizing the first, and finally stabilizing both pendulums in upright position [11]. However, this control method requires considerable time before both pendulums reach the upright position.

I know that in MPC their exist something like an energy cost function meaning that the terms in the cost function are the values with sign not the absolute values. Is the term related to that?

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