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_{ol}(s) and Plant equation D

_{ol}(s) for an open loop system the transfer function can be expressed as a ratio of polynomials where:

G

_{ol}(s) = b(s)/a(s)and D

_{ol}= c(s)/d(s).

For the

**open loop system**the transfer function T

_{ol}= G

_{ol}(s)D

_{ol}(s) = b(s)c(s)/a(s)d(s), the roots of the characteristic equation (the denominator) of this transfer function cannot have any roots in the RHP.

What i'm confused about is that my notes say "An attempt to cancel unstable roots of a(s) of the plant by using c(s) of the controller will be useless. Although, cancelled,

**physically the unstable pole still remains**. The slightest modelling uncertainty will cause the output to diverge"

This doesn't make sense to me as it seems to be saying that the mathematical modelling of the physical plant doesn't actually fully impact what happens physically. How is this possible? I would think that if you design a controller based off of an equation that counteracts the instability of the other controller, how can this same thing not happen when you physically build the thing?