State Space What does u(.) mean

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In control systems, particularly in state space representation, u(.) denotes the input function that influences the system's state. When tasked with finding a control law u(.), it refers to identifying a function u(t) that, when applied, meets specific output criteria. The notation u(.) indicates that it can be a function of time or other variables. This input function is crucial for steering the state from one point to another, as illustrated by the provided A and B matrices. Understanding u(.) is essential for effectively designing control systems.
dmorris619
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I am trying to understand what is meant by u(.) in control systems, specifically in regards to state space representation. To give context, " Find a control law u(.) which steers the state of" then a the A and B matrices are given (0; 0) to (1; 0) in one unit of time.

I don't need help solving the problem I just want to understand what is meant by u(.)
 
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u(.) is the input function. When they say "find a control law u(.) ..." they are asking you to find a function u(t) that when applied at the system input achieves some desired output specifications.
 
So the dot just means any variable?
 
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