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IEVref:351-41-08ID:
Language:enStatus: Standard
Term: state variable
Synonym1:
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Definition: element of a vector x(t) in a system with the differential equations

x ˙ ( t )=f[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadAgadaWadaqaaiaadIhadaqadaqaaiaadshaaiaawIcacaGLPaaacaGGSaGaaGPaVlaaykW7caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaacaGLBbGaayzxaaaaaa@477A@ state equation
v( t )=g[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGNbWaamWaaeaacaWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaaiilaiaaykW7caaMc8UaamyDamaabmaabaGaamiDaaGaayjkaiaawMcaaaGaay5waiaaw2faaaaa@4770@ output equation,

and for linear systems

x ˙ ( t )=Ax( t )+Bu( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadgeacqGHflY1caWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaey4kaSIaamOqaiabgwSixlaadwhadaqadaqaaiaadshaaiaawIcacaGLPaaaaaa@47DA@ state equation
v( t )=Cx( t )+Du( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGdbGaeyyXICTaamiEamaabmaabaGaamiDaaGaayjkaiaawMcaaiabgUcaRiaadseacqGHflY1caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaaaa@47D3@ 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 = Φxi + Huistate equation
vi = Cxi + Duioutput 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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