Stabilization through nonnegative control

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I will have to work on a project about stabilization through nonnegative control. I got some articles about it, which mainly talk about controllability. But, why do we even want stabilization through nonnegative control?

$$\dot{x} = Ax+Bu$$

I know it means that input $u$ is positive, but why do we want this $u$ to be positive?

Hope somebody can help me :)

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Consider the quantity of an antibiotic or other drug that is given to a patient, or or the dose of radiation that is given.