balreal

balanced realization

Calling Sequence

[slb [,U] ] = balreal(sl)

Arguments

:sl,slb linear systems ( syslin lists) :

Description

Balanced realization of linear system sl=[A,B,C,D]. sl can be a continuous-time or discrete-time state-space system. sl is assumed stable.

slb=[`inv`_(U)*A*U ,`inv`_(U)*B , C*U , D]

is the balanced realization.

slb is returned as a syslin list.

Examples

A=`diag`_([-1,-2,-3,-4,-5]);B=`rand`_(5,2);C=`rand`_(1,5);
sl=`syslin`_('c',A,B,C);
[slb,U]=balreal(sl);
Wc=`clean`_(`ctr_gram`_(slb))
W0=`clean`_(`obs_gram`_(slb))

See Also

• ctr_gram controllability gramian
• obs_gram observability gramian
• hankelsv Hankel singular values
• equil balancing of pair of symmetric matrices
• equil1 balancing (nonnegative) pair of matrices