User`s guide

2 LTI Models
2-2
Introduction
The Control System Too lbox offers ex tensiv e to ols to manip ulate and anal yze
linear time-invariant (LTI) models. It supports b oth continuous- and
discrete - time systems. Systems ca n be si n gle- inp ut/s in g le-o u tpu t (S I SO) or
multiple-input/multiple-output(MIMO).In addition, you can store severalLTI
models in an arrayund er a single variable name. See Chapt er 4, “Arrays of LTI
Models” for inf ormati on o n L TI arrays.
This section introduceskey concepts about the MATLAB representation of LTI
models, including LTI objects, precedence rules for operations, and an analogy
between L TI systems and matrices. In addition, it summarizes the basic
commands you can use on LTI objects.
LTI Models
You can specify LTI models as:
• Transfer functions (TF), for example,
• Zero-pole-gain models (ZPK), for example,
• State- sp ace models (SS), for ex ample,
where A, B, C,andDare matrices of appropriate dimensions, x is the sta te
vector, and u and y are the input and output vectors.
• Frequency response data (FRD) models
FRD models consist of sampled measurements of a system’s frequency
response. For example, you can store experimentally collected frequency
response data in an FRD.
Ps()
s 2
+
s
2
s 10++
---------------------------=
Hz()
2z 0.5–()
zz 0.1+()
-------------------------
z
2
z 1++()
z0.2+()z0.1+()
---------------------------------------------
=
xd
td
------ Ax Bu+=
yCxDu+=