User`s guide

6 Time Series Model Identification
Estimating State-Space Time-Series Models
In this section...
“Definition of State-Space Time-Series Model” on page 6-12
“Estimating State-Space M odels at the Command Line” on page 6-12
Definition of State-Space T ime-Series Model
The discrete-time state-space model for a time series is given by the following
equations:
x kT T Ax kT Ke kT
ykT CxkT ekT
( ) () ()
() () ()
+= +
=+
where T is the sampling interval and y(kT) is the output at time instant kT.
The time-series structure corresponds to the general structure with empty B
and D matrices.
For information about general discrete-time and continuous-time structures
for state-space models, see “What Are State-Space Models?” on page 3-73.
Estimating State-Space Models at the Command Line
You can estimate single-output and multiple-output s tate-space models at the
command line for time-domain and frequency-domain d ata (
iddata object).
The following table provides a briefdescriptionofeachcommand. The
resulting models are
idss model objects.
6-12