sigma(sys) singular value plot in Octave for a MIMO System

[paramaniac]

Dear Octave Community

I wrote a model of a simplified heat exchanger and I tried to plot its
singular values over a range of frequencies. In Matlab, there's a command
called sigma(sys) that does the job conveniently. However, I haven't found
an equivalent in Octave yet. So I tried to write a routine by hand, but I
failed miserably ;-) The only thing I managed to compute was the singular
values at a fixed frequency. Does somebody know how to plot them over a
whole range of frequencies, say logspace(-3,1,1000)?

Thanks in advance for every help
Regards
Lukas

% Heat Exchanger

clear all;
close all;
clc;

% Physical Parameters
m_star_1 = 0.5;  % kg/s
m_star_2 = 0.2;  % kg/s
V_1 = 0.01;      % m^3
V_2 = 0.02;      % m^3

rho = 1000;      % kg/m^3
c = 4200;        % J/(kg K)
Ar = 2;          % m^2
k = 2000;        % W/(m^2 K)


% Control-Oriented Parameters
tau_1 = rho * V_1 * c / ( m_star_1 * c  +  k * Ar );
tau_2 = rho * V_2 * c / ( m_star_2 * c  +  k * Ar );

sigma_1 = k * Ar / ( m_star_1 * c  +  k * Ar );
sigma_2 = k * Ar / ( m_star_2 * c  +  k * Ar );

beta_1 = m_star_1 * c / ( m_star_1 * c  +  k * Ar );
beta_2 = m_star_2 * c / ( m_star_2 * c  +  k * Ar );


% System Matrices
A = [      -1/tau_1    sigma_1/tau_1 ;
      sigma_2/tau_2         -1/tau_2 ];
      
B = [ beta_1/tau_1               0 ;
                 0    beta_2/tau_2 ];
             
C = [ 1    0 ;
      0    1 ];
      
D = [ 0    0 ;
      0    0 ];
      

sys = ss(A,B,C,D);


w_0 = 0.1 %logspace(-3,1,1000)   % rad/s

P = C * inv(i*w_0*eye(2) - A) * B  +  D

sigma = svd(P)
sigma_max = sigma(1)
sigma_min = sigma(2)

semilogx(sigma_max, w_0, sigma_min, w_0)

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