There is a mixture of coding styles there. Some good, some bad:

• Always use three parameter open and lexical file handles
  good: open my $fi, "<", $portScanFileIn or die "...";
  bad: open LOG, ">>$backup_log" or die "...";
• Always use explicit loop variables
  good: for my $ip (@ssh_queue) {
  bad: foreach (@filtered_portscan)

In many places you test if (!defined $match) { after using (the possibly undefined) $match in earlier tests. Check that the order of your tests makes sense.

An if that ends in a return doesn't need an else. Instead:

if (...) {
    ...
    return;
}

... # "else" stuff
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In many places you print to stdout and to a log file. Why not have a log sub that prints to both?

Don't put the loop body on the same line as the loop statement. The loop construct as a statement modifier is ok though:

while (<$channel>) {push @output, $_}
#becomes
push @output, $_ while <$channel>;
#although
my @output = <$channel>;
#is even better
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    for my $i (@show_inventory) {
        my $inv_line1 = shift @show_inventory;
        my $inv_line2 = shift @show_inventory;
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is plain wrong. Maybe you meant:

    while (@show_inventory) {
        my $inv_line1 = shift @show_inventory;
        my $inv_line2 = shift @show_inventory;
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