## 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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