Would be Drupal a good choice for my web app? I have a 'webapp' that consists basically of making Linux command line calls; let's admit it runs the 'uptime' command and returns the output.

My app is currently built using CodeIgniter; it works fine, but i'd like to use the powerful features of Drupal that are built-in like users handling, views, imagecache etc.

My main concept is having a 'button' on which user clicks and then it runs the selected task (asynchronously, AJAX) and then shows the result (with jQuery).

I know of 'triggers' but I can't really think of having them 'do' some action once a 'button' (a link) is pressed, not a 'on node creation do ...'.

I just wonder if anyone has done something similar, and how.
Both codeigniter and drupal are php frameworks. Can you elaborate more on what exactly you are looking for? Drupal is capable of doing everything a php can do. Also Drupal 7 has built in ajax support for forms. With additional modules like ctools, you can extend ajax functionality to any DOM elements.

There is Rules module that is more powerful and extended version of triggers. Its the GUI version of if-else-then php statements.