Specifications

balreal
16-20
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 grammians
minreal Minimal realizations
modred Model 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] Moore, B., “Principal Component Analysis in Linear Systems:
Controllability, Observability, and Model Reduction,” IEEE Transactions on
Automatic Control, AC-26 (1981), pp. 17–31.
[3] Laub, A.J., “Computation of Balancing Transformations,” Proc. ACC,San
Francisco, Vol.1, paper FA8-E, 1980.
W
c
TW
c
T
T
= , W
o
T
T–
W
o
T
1–
=
T
W
c
W
o
diag g
()
==