Non-Stable System

A system is said to be stable if its output remains bounded for any bounded input. However, if a system does not have a bounded output for bounded input, then it is said to be a non-stable system.

Explanation:

A system can be represented by its input-output relationship, which is described by a mathematical function or equation. The input to the system is the independent variable, and the output is the dependent variable. The input can be a signal, a set of signals, or any other physical quantity, while the output can be the response of the system to the input.

In a stable system, if the input is bounded, then the output should also be bounded. This means that the response of the system should not grow unbounded or oscillate indefinitely. However, in a non-stable system, the output may grow unbounded or oscillate indefinitely even for a bounded input.

For example, consider an amplifier with positive feedback. If the gain of the amplifier is larger than one, then the output will be fed back to the input with a larger amplitude, which will amplify the output further. This positive feedback loop can lead to an unbounded output even for a bounded input, making the system non-stable.

In practical systems, non-stability can lead to catastrophic consequences, such as amplifier oscillations, motor failures, or even system crashes. Therefore, it is essential to design and analyze the stability of a system before implementing it in real-world applications.

Conclusion:

In summary, if a system does not have a bounded output for bounded input, then it is said to be a non-stable system. Non-stability can lead to catastrophic consequences in practical systems, making stability analysis an essential step in system design and analysis.