Function File: SYS_TRANSFORMED = ss2ss (SYS, T)

Function File: [A_TRANSFORMED B_TRANSFORMED C_TRANSFORMED D_TRANSFORMED] = ss2ss (A, B, C, D, T)

Applies the similarity transformation T to a state-space model

Given the state space model

      .
      x = Ax + Bu
      y = Cx + Du

and the transformation matrix T, which maps the state vector x to another coordinate system

      _
      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

      .
      _            _ 
      x = T A T^-1 x + T B u
      .          _
      y = C T^-1 x + D u

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

      _    -1
      x = T  x

References:

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

https://de.mathworks.com/help/control/ref/ss2ss.html

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

Package: control