I have desined a linear controller in frequency domain,C(s).As my plant is in time domain,I need to transform C(s) into C(t) by inverse Laplace transform.

According to the diagram given below,in frequency domain,the relationship between error(e) and input(u) can be represented by u(s)=C(s)e(s).My question is that,after transformation,does the eqation，u(t)=C(t)e(t),exist?If not,how to express input(u) by C(t)?