Is there a literal asterisk in your filename, or do you want to expand the asterisks in your example? If the latter, I echo Perlbotics' advice to use localtime() and sprintf() to get the date, and suggest you do something like:

foreach my $filename (<AAAA*$date*.log>) {
  ...
}
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Check out the glob() builtin and the <> operator in perlop for more information.