Are all IIR filters unstable in nature?

1. Are all IIR filters unstable?
2. Why IIR filters are unstable?
3. How do I know if my IIR filter is stable?
4. Can linear phase IIR filters be stable?

Are all IIR filters unstable?

Impulse response of FIR filters are always bounded and hence they are inherently stable. On the other hand, an IIR filter may become unstable if not designed properly.

Why IIR filters are unstable?

So, for unstable filters, the impulse response is not absolutely summable. In another way, the impulse response never approaches zero. Again, for IIR filter, h[h] continues to go on with n i.e. never goes to zero. So, IIR filters are supposed to be unstable.

How do I know if my IIR filter is stable?

The stability of an IIR filter can be analyzed by the zero-pole plot of the filter's transfer function. A digital filter is stable if and only if all the poles of the irreducible filter transfer function lie inside the unit circle in the z plane.

Can linear phase IIR filters be stable?

A BIBO stable filter must have its poles within the unit circle, and as such in order to get linear phase, an IIR would need conjugate reciprocal poles outside of the unit circle, making it BIBO unstable.