How to solve multiple LMIs?

I have four inequalities and I need to minimise a parameter 'rho':

1.) AX+BW+constant*X+const*(HH') X' X -I

2.) AX+BW H X' H' -rho*I 0 X 0 -rho*I

3.) const.*I W W' const.*X

4.) const.I const. const. -X

The inequalities are: 1.) <0 2.) <0 3.) <0 4.) <0

And I need to minimise rho.

I have been trying to read the documentation for writing the code for this, but it seems like i cannot figure it out. Kindly help or suggest.