Logics for resource control over time

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I'm studying proof theory and I've seen that linear logic can be used as a "way" to control resources usage, since by the propositions-as-types it is equivalent to the linear lambda calculus.

Is there a logics that allows resource control (like linear logic) and can express properties that vary over a notion of time like linear time temporal logics (LTL)?

Any reference or point to literature is highly appreciated.