balreal

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