IEVref:351-41-08ID:
Language:enStatus: Standard
Term: state variable
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Definition: element of a vector x(t) in a system with the differential equations

 $\stackrel{˙}{x}\left(t\right)=f\left[x\left(t\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}u\left(t\right)\right]$ state equation $v\left(t\right)=g\left[x\left(t\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}u\left(t\right)\right]$ output equation,

and for linear systems

 $\stackrel{˙}{x}\left(t\right)=A\cdot x\left(t\right)+B\cdot u\left(t\right)$ 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.

Publication date:2013-11
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