A state-space model can be physically implemented in hardware, Rugh.

If a transfer function is realisable then there exists a corresponding state-space formulation.

Hence, realisability is a sufficient condition for physical implementability.

Is realisability also a necessary condition? If not, can you give me an example?

  • $\begingroup$ In an ideal, noiseless world, a differentiator is physically implementable. However, it is not realizable, as its transfer function is not proper. $\endgroup$ – Rodrigo de Azevedo Jul 10 '18 at 18:28

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