## Definition of stable system:

An infinite system is BIBO stable if and only if every bounded input produces bounded output.

Mathematical representation:

Let us consider some finite number Mx whose value is less than infinite. That means Mx < 8, so it’s a finite value. Then if input is bounded, we can write,

|x(n)| = Mx < 8

Similarly for C.T. system

|x(t)| = Mx < 8

Similarly consider some finite number My whose value is less than infinity. That means My < 8, so it’s a finite value. Then if output is bounded, we can write,

|y(n)| = My < 8

Similarly for continuous time system

|y(t)| = My < 8

## Definition of Unstable system:

An initially system is said to be unstable if bounded input produces unbounded (infinite) output.

Significance:

- Unstable system shows erratic and extreme behavior.
- When unstable system is practically implemented then it causes overflow.

## Solved problem on stability:

Determine whether the following discrete time functions are stable or not.

1) y(n) = x(-n)

Solution: we have to check the stability of the system by applying bounded input. That means the value of x(-n) should be finite. So when input is bounded output will be bounded. Thus the given function is Stable system.

You may also like:

- Introduction to Signals and Systems
- Causal and Noncausal System (Causality Property)
- Linear or Non-linear Systems (Linearity Property)
- Time Variant or Time Invariant Systems
- Static or dynamic systems

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## 7 Comments

Helfpul... Quite easily addressed.?

ReplyDeleteThanks!

ReplyDeleteOne question... If we apply an unbounded input... And still the output obtained is bounded.. Then what about the stability??

ReplyDeleteSystem will be Unstable

ReplyDeleteCan you give us an example of unstable system !?

ReplyDeleteexp^t

ReplyDeleteexp^t

ReplyDelete