Fig. 4

Visualization of the impact of DC and lack thereof on the output using time-varying step-like changes in the reference input r(t) and disturbance d(t) in different combinations. Gaussian noise was added to the constant value of r(t) and d(t) during certain periods to ensure excitation. y(t) and z(t) show the comparison of the step response when b is 0.3 and 0.6. The output y(t) differs and the difference (green dashed line) is non-zero. A hallmark of the system is not being \(\mathbb {P}\)-invariant with regard to b