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Function Reference: @ss/ss2ss

Function File: SYS_T = ss2ss (SYS, T)
Function File: [A_T B_T C_T D_T] = ss2ss (A, B, C, D, T)

Applies the similarity transformation T to a state-space model

Given the state space model $$ \dot x = Ax + Bu $$$$ y = Cx + Du $$

and the transformation matrix T, which maps the state vector x to another coordinate system $$ \bar{x} = Tx $$

the state-space model is transformed in a way that results in an equivalent state-space model which is based on the new state vector

$$ \dot{\bar{x}} = TAT^{-1}\bar{x} + TBu $$$$ y = CT^{-1}\bar{x} + Du $$

Please note: In the literature, T may be defined inversely:

$$ \bar{x} = T^{-1}x $$


Control System Design, page 484 by Goodwin, Graebe, Salgado, 2000

Attention: T as defined by Matlab is the inverse of T as defined by Goodwin, Graebe, Salgado

Source Code: @ss/ss2ss