The LMI Editor
lmiedit is a graphical user interface
(GUI) to specify LMI systems in a straightforward symbolic manner. Typing
calls up a window with several editable text areas and various buttons.
In more detail, to specify your LMI system,
Declare each matrix variable (name and structure) in the
upper half of the worksheet. The structure is characterized by its type
S for symmetric block diagonal,
G for other structures) and by an
additional “ structure” matrix. This matrix contains specific
information about the structure and corresponds to the second argument of
lmivar (see Specifying the LMI Variables for
Please use one line per matrix variable in the text editing areas.
Specify the LMIs as MATLAB® expressions in the lower half of the worksheet. For instance, the LMI
is entered by typing
[a'*x+x*a x*b; b'*x -1] < 0
x is the name given to the matrix variable
X in the upper half of the worksheet. The left- and
right-hand sides of the LMIs should be valid
Once the LMI system is fully specified, the following tasks can be performed by clicking the corresponding button:
Visualize the sequence of
lmiterm commands needed to
describe this LMI system (
view commands button). Conversely,
the LMI system defined by a particular sequence of
lmiterm commands can be
displayed as a MATLAB expression by clicking on the describe... buttons.
Save the symbolic description of the LMI system (
button). This description can be reloaded later on by clicking the load button.
Read a sequence of
lmiterm commands from a file
(read button). You can then click on
describe the matrix variables or describe the LMIs to visualize the symbolic
expression of the LMI system specified by these commands. The file should
describe a single LMI system but may otherwise contain any sequence of
This feature is useful for code validation and debugging.
This is helpful to develop code and prototype MATLAB functions based on the LMI Lab.
Generate the internal representation of the LMI system by clicking create. The result is written in a MATLAB variable named after the LMI system (if the “name of the
LMI system” is set to
mylmi, the internal
representation is written in the MATLAB variable
mylmi). Note that all LMI-related data
should be defined in the MATLAB workspace at this stage.
The internal representation can be passed directly to the LMI solvers or any other LMI Lab function.
lmiterm, you can use various
shortcuts when entering LMI expressions at the keyboard. For instance, zero blocks
can be entered simply as
0 and need not be dimensioned.
Similarly, the identity matrix can be entered as
dimensioning. Finally, upper diagonal LMI blocks need not be
fully specified. Rather, you can just type (
*) in place of each
Parentheses cannot be used around matrix variables. For instance, the expression
(a*x+b)'*c + c'*(a*x+b)
is invalid when x is a variable name. By contrast,
(a+b)'*x + x'*(a+b)
is perfectly valid.
if statements are ignored.
lmiterm commands into a
symbolic description of the LMI system, an error is issued if the first
lmiterm cannot be
evaluated. Use the LMI and variable identifiers supplied by
lmivar to avoid such