Editing Minimal realization

In [[control theory]], given any [[transfer function]], any [[state space (controls)|state-space]] model that is both [[controllability|controllable]] and [[observability|observable]] and has the same input-output behaviour as the [[transfer function]] is said to be a '''minimal realization''' of the [[transfer function]].<ref>{{citation|title=Linear State-Space Control Systems|first1=Robert L. II|last1=Williams|first2=Douglas A.|last2=Lawrence|publisher=John Wiley & Sons|year=2007|isbn=9780471735557|page=185|url=https://books.google.com/books?id=UPWAmAXQu1AC&pg=PA185}}.</ref><ref name="tan">{{citation|title=Principles of System Identification: Theory and Practice|first=Arun K.|last=Tangirala|publisher=CRC Press|year=2015|isbn=9781439896020|page=96|url=https://books.google.com/books?id=aUHOBQAAQBAJ&pg=PA96}}.</ref>  The realization is called "minimal" because it describes the system with the minimum number of states.<ref name="tan"/>

The minimum number of state variables required to describe a system equals the order of the differential equation;<ref>{{harvtxt|Tangirala|2015}}, p.&nbsp;91.</ref> more state variables than the minimum can be defined. For example, a second order system can be defined by two or more state variables, with two being the minimal realization.

== Gilbert's realization ==
Given a matrix transfer function, it is possible to directly construct a minimal state-space realization by using Gilbert's method (also known as Gilbert's realization).<ref>{{Cite book|title=Robust control systems: theory and case studies|last=Mackenroth, Uwe.|date = 17 April 2013|isbn=978-3-662-09775-5|location=Berlin|pages=114–116|oclc=861706617}}</ref>

==References==
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[[Category:Control theory]]


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