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To counteract this problem, classical control theory uses the [[Laplace transform]] to change an Ordinary Differential Equation (ODE) in the time ___domain into a regular algebraic polynomial in the transform ___domain. Once a given system has been converted into the transform ___domain it can be manipulated with greater ease.
[[Modern control theory]], instead of changing domains to avoid the complexities of time-___domain ODE mathematics, converts the differential equations into a system of lower-order time ___domain equations called [[state space (control)|state equations]], which can then be manipulated using techniques from linear algebra.<ref>{{cite book|last1=Ogata|first1=Katsuhiko|title=Modern Control Systems|date=2010|publisher=Prentice Hall|isbn=978-0-13-615673-4|page=2|edition=Fifth|quote=modern control theory, based on time-___domain analysis and synthesis using state variables}}</ref>
==Laplace transform==
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