Specifications

balreal
16-17
16balreal
Purpose Input/output balancing of state-space realizations
Syntax sysb = balreal(sys)
[sysb,g,T,Ti] = balreal(sys)
Description sysb = balreal(sys) produces a balanced realization sysb of the LTI model
sys with equal and diagonal controllability and observability grammians (see
gram for a definition of grammian). balreal handles both continuous and
discrete systems. If
sys is not a state-space model, it is first and automatically
converted to state space using
ss.
[sysb,g,T,Ti] = balreal(sys) also returns the vector g containing the
diagonal of the balanced grammian, the state similarity transformation
used to convert
sys to sysb, and the inverse
transformation .
If the system is normalized properly, the diagonal
g of the joint grammian can
be used to reduce the model order. Because
g reflects the combined
controllability and observability ofindividual states ofthe balanced model, you
can delete those states with a small
g(i) while retaining the most important
input-output characteristics of the original system. Use
modred to perform the
state elimination.
Example Consider the zero-pole-gain model
sys = zpk([-10 -20.01],[-5 -9.9 -20.1],1)
Zero/pole/gain:
(s+10) (s+20.01)
----------------------
(s+5) (s+9.9) (s+20.1)
A state-space realization with balanced grammians is obtained by
[sysb,g] = balreal(sys)
The diagonal entries of the joint grammian are
g'
ans =
x
b
Tx=
T
i T
1–
=