Let's say we have a system (for example an integrator) whose step response has a negative slope as shown by the MATLAB code below:
clc;clear ;close all R=47*10^3 C=1*10^-7 num1=[-1] den=[R*C 0] sys1=tf(num1,den) num2= sys2=tf(num2,den) subplot 211 pzmap(sys1) title('pole zero map for pure integrator, with -1 in numerator') subplot 212 pzmap(sys2)%plotting poles and zeros title('pole zero map for integrator, with +1 in numerator') figure subplot 211 step(sys1) title('step response for pure integrator, with -1 in numerator') subplot 212 step(sys2) title('step response for integrator, with +1 in numerator')
sys1 is an ideal integrator and we know that ideal integrators are stable systems.
But what if we replace
-1 in the numerator with
sys2): then the step response slope will be positive: is
sys2 unstable because of the positive slope?