Amazon Linux v 2.0 does support systemd and comes installed by default:

cat /etc/os-release
NAME="Amazon Linux"
VERSION="2.0 (2017.12)"
ID="amzn"
ID_LIKE="centos rhel fedora"
VERSION_ID="2.0"
PRETTY_NAME="Amazon Linux 2.0 (2017.12) LTS Release Candidate"
ANSI_COLOR="0;33"
CPE_NAME="cpe:2.3:o:amazon:amazon_linux:2.0"
HOME_URL="https://amazonlinux.com/"

rpm -qa | grep -i systemd
systemd-libs-219-42.amzn2.4.x86_64
systemd-219-42.amzn2.4.x86_64
systemd-sysv-219-42.amzn2.4.x86_64`

1. First check what Amazon linux version you have runnng on using the command cat /etc/os-release
   2. If it is Amazon Linux Version 2, then it does support systemd and comes installed by default.
   3. If it is Amazon linux version 1, then it doesn't support cause Amazon Linux is ultimately based on an old version of CentOS/RHEL.

if it is version 1 (amazon linux), you just need to switch to any other linux distribution that supports systemd. You can't yum install systemd like a package

The new way is to create systemd unit file for your application or startup script. It may seem like an overkill for simple startup scripts but it is the way that most current Linux distros adopted - Amazon Linux, Redhat, Ubuntu, Debian, they all use systemd so it pays to know how to do it properly.

Have a look here for example: Creating and modifying systemd unit files

Hope that helps :)

Amazon Linux 2

If your version of Amazon Linux is >=2.0, it has systemd by default. In this case, you should simply be able to use the same unit file you have been using on CentOS, with the restart directives.

Amazon Linux AMI

If you are you are running Amazon Linux AMI, you will need to either use a separate supervisor to monitor your process (as poige mentioned), or utilize /etc/inittab.

For example, in order to have sysvinit automatically restart your process, add the following to /etc/inittab:

# Start and respawn process
mydaemon:2345:respawn:/path/to/executable argument1 argument2

This tells sysvinit to start the process on runlevels 2, 3, 4, and 5 and restart it when it terminates.

Also, if you wish to add some commands around the executable to be run on startup, the executable path can instead refer to a script that runs the program in the foreground.

I need to make my application keep on run, so that i need systemd has to be installed on my linux machine

As others have noted, systemd is not available for your version of Amazon Linux. Fortunately, there are other tools than systemd that solve your problem; I suggest looking at cron. You might take a look at this answer for how to set a program or script to run on reboot on an Amazon Linux box. Alternatively, there's always the cron man page, which sould also be on your machine.

systemd is not supported in Services. The only correct is sysvinit:

services:
  sysvinit:
    my_worker:
      enabled: "true"
      ensureRunning: "true"

But I don't think it will even work, as this is for Amazon Linux 1, not for Amazon Linux 2.

In Amazon Linux 2 you shouldn't be even using much of .ebextensions. AWS docs specifically write:

On Amazon Linux 2 platforms, instead of providing files and commands in .ebextensions configuration files, we highly recommend that you use Buildfile. Procfile, and platform hooks whenever possible to configure and run custom code on your environment instances during instance provisioning.

Thus, you should consider using Procfile which does basically what you want to achieve:

Use a Procfile for long-running application processes that shouldn't exit. Elastic Beanstalk expects processes run from the Procfile to run continuously. Elastic Beanstalk monitors these processes and restarts any process that terminates. For short-running processes, use a Buildfile.

Alternative

Since you already have created a unit file /etc/systemd/system/my_worker.service for systemd, you can enable and start it yourself.

For this container_commands in .ebextensions can be used. For example:

container_commands:
   10_enable_worker:
     command: systemctl enable worker.service
   20_start_worker:
     command: systemctl start worker.service

It appears the version of Amazon Linux you are using does not have systemd. I'm not sure that any version of Amazon Linux as of today uses systemd. Considering that systemd is a core part of an operating system, it's not something you can just install as a package and expect to work.

If you can't find the packages you need built for Amazon Linux, my recommendation is to start over with an AMI from a different OS. For example, there are AMIs for CentOS that you could start with instead.

I recommend switching to a new Linux distribution. On a more popular Linux distribution like CentOS or Ubuntu, you are far less likely to run into problems with missing packages as you are currently experiencing with Amazon Linux.