User`s guide

State-Space Realizations
5-7
State-Space Realizations
The following functions are useful t o analyze, perform state coordinate
transformations on, and derive canonical state-space realizations for single
state-space LTI models or LTI arrays of state-space models.
The function
ssbal uses a simple diagonal similarity transformation
to balance the state-space data . This is accomplished by reducing
the norm of t he matrix.
Such balancing usually improves the numerical conditioning o f s ubsequent
state-space computations. Note that conversions to state-space using
ss
produce bal anced r eali zati ons of transfe r functi ons and zero-pole-gain mod els.
By contrast, t he canonical realizat ions produced by
canon, ctrbf,orobsvf are
often b ad ly sc al ed, s ens iti ve to pert urbat ions of the d ata , and poorly s uit ed for
State-Space Realizations
canon
Canonical state-space realizations.
ctrb
Controllability matrix.
ctrbf
Controllability staircase form.
gram
Controllability and observability gramians.
obsv
Observability matrix.
obsvf
Observability staircase form.
ss2ss
State coordinate transformation.
ssbal
Diagonal balancing of state-space realizations.
ABC,,()T
1
–
AT T
1
–
BCT,,()→
ABC
,,()
T
1–
AT T
1–
B
CT 0