$\dot{x}\left(t\right)=f\left[x\left(t\right),u\left(t\right)\right]$	state equation
$v\left(t\right)=g\left[x\left(t\right),u\left(t\right)\right]$	output equation,

and for linear systems

$\dot{x}\left(t\right)=A\cdot x\left(t\right)+B\cdot u\left(t\right)$	state equation
$v\left(t\right)=C\cdot x\left(t\right)+D\cdot u\left(t\right)$	output equation,

from which for known initial values of the vector elements at any given instant t₀ (often with t₀ = 0) and known course of the elements of the input vector u(t) the course of the elements of the output vector v(t) may be calculated starting at t₀

SEE: Figure 3.

Note 1 to entry: In case of discrete-time variables the describing equations are

xi+1 = f (xi, ui)	state equation
vi = g (xi, ui)	output equation,

and for linear systems

xi+1 = Φ·xi + H·ui	state equation
vi = C·xi + D·ui	output equation.

Note 2 to entry: This entry was numbered 351-21-08 in IEC 60050-351:2006.