list files ignoring the case option

Sorry if this is a question more on regular expressions. I am dealing
with several files which have been badly named. For example the files
are given either the extensions txt, TXT or Txt. I wish to select all
those files ending with 'txt' ignoring case.

Here is how I would do it in bash (Redhat FC2) :

   touch  a1.txt  a2.TXT  a3.Txt  txt.control  TXT.control
   ls -1 | grep -i "txt$"


Here is how I am currently doing it in R

   a <- list.files(all.files=T)
   grep( "txt$", a, ignore.case=T, value=T )


Is it possible for me to modify the following line to include ignore
case option ?

   a <- list.files( pattern="txt$" )

Thank you.

Regards, Adai