## Specify LMIs with the LMI Editor GUI

The LMI Editor `lmiedit`

is a graphical user interface
(GUI) to specify LMI systems in a straightforward symbolic manner. Typing

lmiedit

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,`R`

for unstructured, and`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 details).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$$\left(\begin{array}{cc}{A}^{T}X+XA& XB\\ {B}^{T}X& -I\end{array}\right)<0$$

is entered by typing

[a'*x+x*a x*b; b'*x -1] < 0

if

`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*MATLAB expressions.

Once the LMI system is fully specified, the following tasks can be performed by clicking the corresponding button:

Visualize the sequence of

`lmivar`

/`lmiterm`

commands needed to describe this LMI system (`view commands`

button). Conversely, the LMI system defined by a particular sequence of`lmivar`

/`lmiterm`

commands can be displayed as a MATLAB expression by clicking on the**describe...**buttons.Beginners can use this facility as a tutorial introduction to the

`lmivar`

and`lmiterm`

commands.Save the symbolic description of the LMI system (

`save`

button). This description can be reloaded later on by clicking the**load**button.Read a sequence of

`lmivar`

/`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 MATLAB commands.This feature is useful for code validation and debugging.

Write in a file the sequence of

`lmivar`

/`lmiterm`

commands needed to describe a particular LMI system (**write**button).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.

### Keyboard Shortcuts

As with `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 `1`

without
dimensioning. Finally,* upper diagonal* LMI blocks need not be
fully specified. Rather, you can just type (`*`

) in place of each
such block.

### Limitations

Though fairly general, `lmiedit`

is not as flexible as
`lmiterm`

and the following
limitations should be kept in mind:

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.

Loops and

`if`

statements are ignored.When turning

`lmiterm`

commands into a symbolic description of the LMI system, an error is issued if the first argument of`lmiterm`

cannot be evaluated. Use the LMI and variable identifiers supplied by`newlmi`

and`lmivar`

to avoid such difficulties.

### How lmivar and lmiterm Manage LMI Representation

Users familiar with MATLAB may wonder how `lmivar`

and `lmiterm`

physically update the
internal representation `LMISYS`

since `LMISYS`

is
not an argument to these functions. In fact, all updating is performed through
global variables for maximum speed. These global variables are initialized by
`setlmis`

, cleared by `getlmis`

, and are not visible in
the workspace. Even though this artifact is transparent from the user's viewpoint,
be sure to: