Incremental Backup

#!/bin/bash
typeset -g BACKUP_STORAGE='/FullPathToYourStorage'
typeset -g PREFIX='backup_'
typeset -g TIME_STAMP=$(date -I)
typeset -g BACKUP_DIR=${BACKUP_STORAGE}/${PREFIX}${TIME_STAMP}
typeset -g PREV
mkdir --parent --verbose ${BACKUP_STORAGE}
if [[ -d ${BACKUP_DIR} ]]
then
  echo 'already updated'
  exit 1
fi

# find least backup
typeset -i time_diff=$(date +'%s') # seconds since 1970-01-01 UTC
typeset -i current_time=$((time_diff))
for dir in ${BACKUP_STORAGE}/${PREFIX}*
do
  prev_time_stamp=$(echo $dir | sed "s;${BACKUP_STORAGE}/${PREFIX};;")
  typeset -i prev_since_utc=$(($(date --date=${prev_time_stamp} +'%s')))
  if (( current_time - prev_since_utc < time_diff ))
  then
    time_diff=$((current_time - prev_since_utc))
    PREV=$dir
  fi
done

# new backup or differential backup
if [[ -z ${PREV} ]]
then
  echo 'new backup'
  rsync --archive --verbose $1 ${BACKUP_DIR}
else
  echo 'differential backup'
  rsync --archive --verbose --link-dest=${PREV} $1 ${BACKUP_DIR}
fi