Firstly if there is no cross beams or struts then your roof may indeed become unstable in the future.
These are installed to take the pressure off the rafters and give extra tolerance for wind force and other weathering conditions.
I know that you have stated that you have lived in the house for over 20 years without any problems but I think that you should still be cautious.
The best thing for you to do would be to have a qualified person come over and make sure that everything is safe and sound.
With regards to cross battening. The best approach to do this is not to cross batten but instead have joists laid in between your existing joists.
The new joists should be placed over raised wall plates (add/fix new wall plates in between joists). These new joists should be at least 8 inches by 2 inches. This will give you a distance from your old joists of a few inches and will not spread weight across your existing ceilings or existing joists.
Remember only do this if the run of your new joists is under 6 meters, if it is above 6 meters then please get a professional to visit your home and advise you properly as you will need an RSJ.
