User`s guide

ctrbf
11-46
Example Compute the controllability staircase form for
A =
1 1
4 –2
B =
1 –1
1 –1
C =
1 0
0 1
and locate the uncontrollable mode.
[Abar,Bbar,Cbar,T,k]=ctrbf(A,B,C)
Abar =
–3.0000 0
–3.0000 2.0000
Bbar =
0.0000 0.0000
1.4142 –1.4142
Cbar =
–0.7071 0.7071
0.7071 0.7071
T =
–0.7071 0.7071
0.7071 0.7071
k =
1 0
The decomposed system Abar shows an uncontrollable mode located at –3 and
a controllable mode located at 2.
Seealsothefunction
minreal, whichusesctrbf tofindtheminimalrealization
of a system.