IEVref: | 351-41-08 | ID: | |||||||||||||||||

Language: | en | Status: Standard | |||||||||||||||||

Term: | state variable | ||||||||||||||||||

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Definition: | element of a vector (xt) in a system with the differential equations
and for linear systems
from which for known initial values of the vector elements at any given instant t) the course of the elements of the output vector (vt) may be calculated starting at t_{0} SEE: Figure 3. Note 1 to entry: In case of discrete-time variables the describing equations are
and for linear systems
Note 2 to entry: This entry was numbered 351-21-08 in IEC 60050-351:2006. | ||||||||||||||||||

Publication date: | 2013-11 | ||||||||||||||||||

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$\dot{x}\left(t\right)=f\left[x\left(t\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}u\left(t\right)\right]$ | 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

$\dot{x}\left(t\right)=A\cdot x\left(t\right)+B\cdot u\left(t\right)$ | 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 *t*_{0} (often with *t*_{0} = 0) and known course of the elements of the input vector ** u**(

SEE: Figure 3.

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

x_{i+1} = (fx_{i}, u_{i}) | state equation |

v_{i} = (gx_{i}, u_{i}) | output equation, |

and for linear systems

x_{i+1} = ·Φx_{i} + ·Hu_{i} | state equation |

v_{i} = ·Cx_{i} + ·Du_{i} | output equation. |

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