Minimal realization

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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.


  1. ^ Williams, Robert L., II; Lawrence, Douglas A. (2007), Linear State-Space Control Systems, John Wiley & Sons, p. 185, ISBN 9780471735557 .
  2. ^ a b Tangirala, Arun K. (2015), Principles of System Identification: Theory and Practice, CRC Press, p. 96, ISBN 9781439896020 .
  3. ^ Tangirala (2015), p. 91.