# mat2dec

Extract vector of decision variables from matrix variable values

## Syntax

```decvec = mat2dec(lmisys,X1,X2,X3,...)
```

## Description

Given an LMI system `lmisys` with matrix variables X1, . . ., XK and given values `X1,...,Xk` of X1, . . ., XK, `mat2dec` returns the corresponding value `decvec` of the vector of decision variables. Recall that the decision variables are the independent entries of the matrices X1, . . ., XK and constitute the free scalar variables in the LMI problem.

This function is useful, for example, to initialize the LMI solvers `mincx` or `gevp`. Given an initial guess for X1, . . ., XK, `mat2dec` forms the corresponding vector of decision variables `xinit`.

An error occurs if the dimensions and structure of `X1,...,Xk` are inconsistent with the description of X1, . . ., XK in `lmisys`.

## Examples

Consider an LMI system with two matrix variables X and Y such that

• X is a symmetric block diagonal with one 2-by-2 full block and one 2-by-2 scalar block.

• Y is a 2-by-3 rectangular matrix.

Particular instances of X and Y are

and the corresponding vector of decision variables is given by

```decv = mat2dec(lmisys,X0,Y0) decv' ans = 1 3 -1 5 1 2 3 4 5 6 ```

Note that `decv` is of length 10 since Y has 6 free entries while X has 4 independent entries due to its structure. Use `decinfo` to obtain more information about the decision variable distribution in X and Y.

## Version History

Introduced before R2006a