Under which conditions an initially relaxed system does becomes unsta...
Only if bounded i/p generates unbounded o/p, in these conditions an initially relaxed system becomes unstable.
BIBO – In this system bounded input produces bounded output. Usually these systems are considered as stable system. This kind of systems are also linear systems i. e. output is directly proportional to the input and at initial state zero output.
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Under which conditions an initially relaxed system does becomes unsta...
Conditions for Instability in Initially Relaxed System
An initially relaxed system can become unstable under certain conditions. Let's discuss those conditions in detail:
Bounded Input Generates Unbounded Output
If a bounded input is given to a system, it should produce a bounded output. Otherwise, the system becomes unstable. This is because the system is not able to handle the input signal properly and produces an unbounded output, which can lead to instability.
Unbounded Input Generates Unbounded Output
If an unbounded input is given to a system, it should produce an unbounded output. If the system produces a bounded output, it becomes unstable. This is because the input signal is too large for the system to handle, and the system produces an output that is not proportional to the input signal.
Bounded Input Generates Bounded Output
If a bounded input is given to a system, it should produce a bounded output. If the system produces an unbounded output, it becomes unstable. This is because the system is not able to handle the input signal properly and produces an output that is not proportional to the input signal.
Conclusion
From the above discussion, we can conclude that an initially relaxed system becomes unstable only if a bounded input generates unbounded output. This is because the system is not able to handle the input signal properly and produces an output that is not proportional to the input signal. Therefore, it is important to ensure that the input signal is within the system's limits to prevent instability.
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