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I have a simple question regarding the realization of systems. In my university course books, it's mentioned multiple times that a system with a transfer function G(s) is realizable, if the denominator's degree is at least that of the numerator's degree. I found the same statement on the internet as well: http://en.wikibooks.org/wiki/Control_Systems/Realizations

I don't understand what exactly this means, and it's always without explanation.

For example, suppose I have a transfer function G(s) = Y(s)/U(s) = Cs, which so shouldn't be realizable physically.

Doesn't a simple capacitor "realize" this transfer functions? If I consider the voltage of the capacitor my input, and the current through it the output? Then i = C*du/dt.

What do we mean by a system being realizable?

Thanks for any help!

-Tusike