Specifications

4 Model Analysis Tools
4-8
State-Space Realizations
The following functions are useful to 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 the matrix.
Such balancing usually improves the numerical conditioning of
subsequent state-space computations. Note that conversions to
state-space using
ss produce balanced realizations of transfer functions
and zero-pole-gain models.
By contrast, the canonical realizations produced by
canon, ctrbf,or
obsvf are often badly scaled, sensitive to perturbations of the data, and
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