A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. Shifting the Galois output ten times to the right, we would find the same output of the Fibonacci LFSR.The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Just for fun, let's try it with a mirroring output. In order to obtain this kind of coupled outputs, the taps of the Galois register must be the counterparts of the ones of the Fibonacci register. The seed choice is not relevant since it would introduce only a shift in the output. In such a register, all possible states are visited - except the null state, which would make the register collapse in a sequence of 0s.

The two types of LFSR produce the same result - minus a reflection and a translation - when the taps are the ones generating a maximally long LFSR.

Linear feedback