Need for Feedback to Stabilize Unstable Systems

This post addresses the following question with the help of an example:

Question: Is it possible to practically stabilize an unstable system without feedback?

Let us consider an unstable system with transfer function P=1s1. This plant has a pole on the right hand side plane in the s-domain, which means it is unstable. A naive (and incorrect way) to stabilize this system will be to employ a controller K=s1s+1 without any feedback. One might argue that the open loop transfer function P×K=1s+1 and the new pole now occurs at left hand plane of the s-domain, so this system must become stable. Unfortunately, it does not, due to at least two reasons:

The disturbances in the plant input and output can completely throw away the stability. This can only be corrected using feedback. Even in a disturbance free ideal world, all numbers are finite precision and have errors. So while computing P×K, the s1 terms in the numerator and denominator cannot completely cancel each other.

Answer: No.

I will put the response of such a system using Matlab to show instability in a future post.