Question 11.15.1: Determine if the LTI system with transfer function H1 (s) = ...
Determine if the LTI system with transfer function
H(s)=\frac{H_1(s)}{H_2(s)}is BIBO stable, where
H_1(s)=\frac{2s^2+1}{s^3+3s^2+3s+1}and
H_2(s)=\frac{(s+1)(s+2)}{(s+2j)(s-2j)(s+3)} .
num1=[1 1];
num2=[1 2];
numH2=conv(num1,num2);
den1=[1 2j];
den2=[1 2j];
den3=[1 3];
den12=conv(den1,den2);
denH2=conv(den12,den3);
First, H_2(s) is expressed in rational form by using the command conv to execute the multiplications of the polynomials of the numerator and denominator of H_2(s).
numH1=[2 0 1];
numH=conv(numH1,denH2);
denH1=[1 3 3 1];
denH=conv(denH1,numH2)
The numerator of H(s) is computed by multiplying (using conv) the numerator polynomial of H_1(s) with the denominator polynomial of H_2(s). The corresponding operation is done to obtain the denominator of H(s).
H(s) is defined as a TF object, the poles are computed, and (together with the zeros) are plotted.
H=tf(numH,denH);
poles=pole(H)
pzmap(H)
The poles are at the left half of the complex plane (as their real part is negative); thus the system is BIBO stable.
