1. References

In control theory, given any transfer function, any state-space model that is both controllable and observable and has the same input-output behaviour as the transfer function is said to be a minimal realization of the transfer function.^[1][2] The realization is called "minimal" because it describes the system with the minimum number of states.^[2]

The minimum number of state variables required to describe a system equals the order of the differential equation;^[3] more state variables than the minimum can be defined. For example, a second order system can be defined by two(minimal realization) or more state variables.

References

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• Artin-Verdier duality
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