A state-space representation describes a dynamical system using a state vector whose value at a given time contains the information needed to determine its subsequent evolution. A continuous-time linear time-invariant system is commonly written
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(1)
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(2)
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where 
is the state vector, 
is the input, and 
is the output. The matrix 
specifies the state dynamics, 
gives the effect of the input on the state, 
maps the state to the output, and 
gives the direct effect of the input on the output.
For a discrete-time system, the corresponding equations are
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(3)
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(4)
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