I have a problem in my CVX program, where a convex function:

\eta(x) = a*x*(1+(\frac{x}{b})^4)

is at the left hand side of my constraint. a and b are given constants

The problem is that my x is a norm of a matrix, so convex, and CVX does not accept any of the power functions in order to represent the 4th power of x. I get the following error message:
Disciplined convex programming error:
Illegal operation: pow_p( {concave}, {4} )

The fact that the error says the input to pow_p is concave suggests that it is not the norm of a matrix as you claim it to be.

Regardless, as the help documentation for pow_p states, it can accept only affine inputs. You will have more luck with pow_pos, which is the monotonic extension of pow. Still, that requires a convex input.

But even if you get past that problem, you have another product in your expression that will be forbidden. Your problem is very likely not convex. Please read the FAQ.