Determine if dynamic system model is proper
B = isproper(sys)
B = isproper(sys,'elem')
[B,sysr] = isproper(sys)
B = isproper(sys) returns
a logical value of
if the dynamic system model
sys is proper and a
logical value of
A proper model has relative degree ≤ 0 and is causal.
SISO transfer functions and zero-pole-gain models are proper if the
degree of their numerator is less than or equal to the degree of their
denominator (in other words, if they have at least as many poles as
zeroes). MIMO transfer functions are proper if all their SISO entries
are proper. Regular state-space models (state-space models having
E matrix) are always proper. A descriptor state-space
model that has an invertible
E matrix is always
proper. A descriptor state-space model having a singular (non-invertible)
is proper if the model has at least as many poles as zeroes.
sys is a model array, then
all models in the array are proper.
B = isproper(sys,'elem') checks each model
in a model array
sys and returns a logical array
of the same size as
sys. The logical array indicates
which models in
sys are proper.
[B,sysr] = isproper(sys) also returns an
sysr with fewer states (reduced
order) and a non-singular
E matrix, if
a proper descriptor state-space model with a non-invertible
sys is not proper,
sysr = sys.
Examine Whether Models are Proper
Create a SISO continuous-time transfer function,
H1 = tf([1 0],1);
H1 is proper.
B1 = isproper(H1)
B1 = logical 0
SISO transfer functions are proper if the degree of their numerator is less than or equal to the degree of their denominator That is, if the transfer function has at least as many poles as zeroes. Since
H1 has one zero and no poles, the
isproper command returns
Now create a transfer function with one pole and one zero,
H2 = tf([1 0],[1 1]);
H2 is proper.
B2 = isproper(H2)
B2 = logical 1
H2 has equal number of poles and zeros,
Compute Equivalent Lower-Order Model
Combining state-space models sometimes yields results that include more states than necessary. Use
isproper to compute an equivalent lower-order model.
H1 = ss(tf([1 1],[1 2 5])); H2 = ss(tf([1 7],)); H = H1*H2; size(H)
State-space model with 1 outputs, 1 inputs, and 4 states.
H is proper and reducible.
isproper returns the reduced model.
[isprop,Hr] = isproper(H); size(Hr)
State-space model with 1 outputs, 1 inputs, and 2 states.
Hr are equivalent, as a Bode plot demonstrates.
 Varga, Andràs. "Computation of irreducible generalized state-space realizations." Kybernetika 26.2 (1990): 89-106.