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Specify matrix variables in LMI problem

X = lmivar(type,struct) [X,n,sX] = lmivar(type,struct)

`lmivar`

defines a new matrix
variable * X* in the LMI system currently described.
The optional output

`X`

is an identifier that can
be used for subsequent reference to this new variable.The first argument `type`

selects among available
types of variables and the second argument `struct`

gives
further information on the structure of * X* depending
on its type. Available variable types include:

**type=1:** Symmetric matrices
with a block-diagonal structure. Each diagonal block is either full
(arbitrary symmetric matrix), scalar (a multiple of the identity matrix),
or identically zero.

If * X* has

`struct`

is
an `struct(r,1)`

is the size of the-th block*r*`struct(r,2)`

is the type of the-th block (1 for full, 0 for scalar, –1 for zero block).*r*

**type=2:** Full * m*-by-

`struct = [m,n]`

in this case.**type=3:** Other structures. With
Type 3, each entry of * X* is specified as zero or
±

Accordingly, `struct`

is a matrix of the same
dimensions as * X* such that

`struct(i,j)=0`

if(*X*) is a hard zero*i, j*`struct(i,j)=n`

if(*X*) =*i, j**x*_{n}`struct(i,j)=–n`

if(*X*) = –*i, j**x*_{n}

Sophisticated matrix variable structures can be defined with
Type 3. To specify a variable * X* of Type 3, first
identify how many

`lmivar`

optionally
returns two extra outputs: (1) the total number n of scalar decision
variables used so far and (2) a matrix `sX`

showing
the entry-wise dependence of Was this topic helpful?