In book , 'fundamental of signal and system'by M.J ROBERT it is written that
Since no practical system can ever produce an unbounded response, strictly speaking, all practical systems are stable. The ordinary operational meaning of BIBO instability is a system described approximately by linear equations that would develop an unbounded response to a bounded excitation if the system remained linear. Any practical system will become nonlinear when its response reaches some large magnitude and can never produce a truly unbounded response. So a nuclear weapon is a BIBO-unstable system in the ordinary sense but a BIBO-stable system in the strict sense. Its energy release is not unbounded even though it is extremely large compared to most other artificial systems on earth
For a given LTI system, what parameter of system along with input which determines the maximum magnitude of response after which it becomes non linear and how to calculate this maximum magnitude of response mathematically?