Specifications

2 LTI Models
2-16
In addition to the A, B, C,andD matrices, the display of state-space models
includes state names, input names, and output names. Default names (here,
x1, x2, u1,andy1) are displayed whenever you leave these unspecified. See
“LTI Properties” on page 2-25 for more information on how to specify state,
input, or output names.
Descriptor State-Space Models
Descriptor state-space (DSS) models are a generalization of the standard
state-space models discussed above. They are of the form
The Control System Toolbox supports only descriptor systems with a
nonsingular matrix. While such models have an equivalent explicit form
it is often desirable to work with the descriptor form when the matrix is
poorly conditioned with respect to inversion.
The function
dss is the counterpart of ss for descriptor state-space models.
Specifically,
sys = dss(A,B,C,D,E)
creates a continuous-time DSS model with matrix data A,B,C,D,E.For
example, consider the dynamical model
withvector ofangular velocities. Iftheinertiamatrix is poorly conditioned
with respect to inversion, you can specify this system as a descriptor model by
sys = dss(–F,eye(n),eye(n),0,J) % n = length of vector
E
xd
td
------
Ax Bu+=
yCxDu+=
E
xd
td
------
E
1–
A
()
xE
1–
B
()
u+=
yCxDu+=
E
J
d
ω
dt
--------
F
ω
+ T=
y
ω
=
ω J
ω