Install required packages:

diffstat chrpath socat libtool libtool-bin libncurses5-dev libssl-dev zlib1g-dev

gcc net-tools make autoconf git

And ncurses:

libncurses5 libncursesw5

Set bash as default shell:

dpkg-reconfigure dash 

PetaLinux needs a patch for sed (in Debian Strech bash and sed are too new for PetaLinux).
From Xilinx forum: “The problem is the “ls | sed” command sequence in the last line generates a multi-line response while the bash read builtin only reads a single line. I added a wrapper around sed that translates the newlines generated into spaces and the installer completed as expected on an otherwise stock Debian stretch install.” – the default Xilinx workaround is to… replace the system sed with the wrapper, which is really nasty solution. Let's make it properly:
Create sed path script (assume example name sed.sh) and make it executable:

#!/bin/sh 
# Remove newlines if called by the silly Xilinx PetaLinux 2018.1 installer
if [ "$2" = "s/^.*minimal-\(.*\)-toolchain.*/\1/" ] ; then
   /bin/sed "$@" | tr '\n' ' '
else
   /bin/sed "$@"
fi 

Create source script which will later set the PetaLinux environment. Assume example name settings_petalinux_2018.3.sh:

alias sed="<path_to_sed_wrapper_script>/sed.sh"

Download PetaLinux from Xilinx - PetaLinux version have to match the installed Vivado version:
https://www.xilinx.com/support/download/index.html/content/xilinx/en/downloadNav/embedded-design-tools.html

Source the settings_petalinux_2018.3.sh script.

Run downloaded PetaLinux installer:

./petalinux-v2018.3-final-installer.run <path_to_PetaLinux_target_directory>

It seems to be better to install the PetaLinux as user in user-accessible directory, not as root in /opt/.

Modify the settings_petalinux_2018.3.sh script and add the source of PetaLinux environment:

source <path_to_PetaLinux_target_directory>/settings.sh

In order to use the PetaLinux, source the settings_petalinux_2018.3.sh script.