Specifications

2 LTI Models
2-2
The Control System Toolbox offers extensive tools to manipulate and analyze
linear time-invariant (LTI) models. It supports both continuous- and
discrete-time systems. Systems can be single-input/single-output (SISO) or
multiple-input/multiple-output(MIMO).In addition, you can store severalLTI
models in an array under asingle variable name. SeeChapter 4, “Arrays of LTI
Models” for information on LTI arrays.
This section introduces key concepts about the MATLAB representation ofLTI
models, including LTI objects, precedencerules for operations, and an analogy
between LTI 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-space models (SS), for example,
where A, B, C,andD are matrices of appropriate dimensions, x is the state
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
()
2 z 0.5–
()
zz 0.1+
()
-------------------------
z
2
z 1++
()
z 0.2+
()
z 0.1+
()
---------------------------------------------
=
xd
td
------
Ax Bu+=
yCxDu+=