User`s guide

balreal
11-18
Algorithm Consider the model
with controllability and observability gramians and . The state
coordinate transformation produces the equivalent model
and transforms the gramians to
The function
balreal computes a particular similarity transformation such
that
See [1,2] for details on the algorithm.
Limitations The LTI model sys must be stable. In addition, controllability and
observability are required for state-space models.
See Also gram Controllability and observability gramians
minreal Minimal realizations
modred M odel order reduction
References [1]Laub,A.J.,M.T.Heath,C.C.Paige,andR.C.Ward,“ComputationofSystem
Balancing Transformations and Other Applications of Simultaneous
Diagonalization Algorithms,” IEEE Trans. Automatic Control, AC-32 (1987),
pp. 115–122.
[2] Moo re, B., “P rincipal Component Analysis in Linear Systems :
Controllability, Obs ervability , and Model Reductio n,” IEEE Transactions on
Automatic Control, AC-26 (1981), pp. 17–31.
[3] Laub, A.J., “Comp utation of Balancing Transformations,” Proc. ACC,San
Francisco, Vol.1, paper FA8-E, 1980.
x
·
Ax Bu+=
yCxDu+=
W
c
W
o
xTx=
x
·
TAT
1–
xTBu+=
yCT
1–
xDu+=
W
c
TW
c
T
T
= , W
o
T
T
–
W
o
T
1
–
=
T
W
c
W
o
diag g()==