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of and .If the system is controllable then these two vectors can span the entire plane and can be done so for time .

The assumption made that the initial state is zero is merely for convenience. Clearly if all states can be reached from the origin then any state can be reached from another state (merely a shift in coordinates).

This example holds for all positive , but the case of is easier to visualize.

Analogy for example of = 2

Consider an analogy to the previous example

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