User`s guide

3 Linear Model Identification
Definition of State-Space M odels
State-space models are models that use state variables to describe a system by
asetoffirst-order differential or difference equations, rather than by one or
more nth-order differential or difference equations. State variables x(t) can be
reconstructed f rom the measured inpu t-output data, but are not themselves
measured during an experiment.
The state-space model structure is a good choice for quick estimation because
it requires only two parameters:
•
n — Model order or the number of poles (size of the A matrix).
•
nk — One or more input delays.
The model order for state-space models is an integer equal to the dimension
of x(t) and relates to the number of delayed inputs and outputs used in the
corresponding linear difference equation.
Continuous-Time Representation
In continuous-time, the state-space description has the following form:


xt Fxt Gut Kwt
yt Hxt Dut wt
xx
() () () ()
() () () ()
()
=++
=++
=00
It is ofte n easier to define a parameterized state-space model in continuous
time because p hysical laws are most often described in t erms of differential
equations. In this case, the matrices F , G, H,andD contain e lements with
physical significance—for example, m aterial constants. x0 specifies the initial
states.
Note K=0 gives the state -space representation of an Output-Error m odel.
For more information about Output-Error models, see “What Are Black-Box
Polynom ial M odels?” on page 3-41.
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