Routh-Hurwitz Stability Criterion

[The Valkyrie]

With the help from people from forum.hr, I have modified the code of my program like this:

Code:

Function obrni_polinom() Which Returns Nothing Is Declared;

Function f(Integer16 i, Integer16 j) Which Returns Integer16 Does
  // Za pretvaranje indeksa dvodimenzionalnog polja u indeks jednodimenzionalnog
  // polja. Kada u svoj AEC compiler još nisam implementirao dvodimenzionalna
  // polja...
  Return 20 * i + j;
EndFunction

Function popuni_matricu() Which Returns Integer16 Does
  Integer16 broj_stupaca :=
              (stupanj_polinoma + 1) / 2 + mod(stupanj_polinoma + 1, 2),
            broj_redaka := stupanj_polinoma + 1;
  Integer16 i := 0;
  //Popunimo matricu prvo not-a-numbersima...
  While i < broj_redaka Loop
    Integer16 j := 0;
    While j < broj_stupaca Loop
      matrica[f(i, j)] := 0. / 0.;
      j += 1;
    EndWhile
    i += 1;
  EndWhile
  //Zatim idemo primjeniti Hurwitzov algoritam...
  i := 0;
  While i < broj_redaka Loop
    Integer16 j := 0;
    While j < broj_stupaca Loop
      If i = 0 Then // Prvi redak
        matrica[f(i, j)] := polinom[j * 2];
      ElseIf i = 1 Then // Drugi redak
        matrica[f(i, j)] := (j * 2 + 1 < stupanj_polinoma + 1) ?
                            polinom[j * 2 + 1] :
                            0;
      Else // Ostali reci...
        If matrica[f(i - 1, 0)] = 0 Then // Posebni slučajevi, kada se u prvom
                                         // stupcu matrice pojavi nula.
          If jesmo_li_obrnuli_polinom Then // Obrtanje polinoma nije "upalilo".
            Return 0;
          Else // Možda obrtanje polinoma "upali"...
            obrni_polinom(); // https://www.forum.hr/showpost.php?p=97955497&postcount=16
            jesmo_li_obrnuli_polinom := 1;
            Return popuni_matricu();
          EndIf
        EndIf
        matrica[f(i, j)] := (matrica[f(i - 1, 0)] *
                            (j + 1 < broj_stupaca ?
                             matrica[f(i - 2, j + 1)] : 0) -
                            (matrica[f(i - 2, 0)] *
                            (j + 1 < broj_stupaca ?
                             matrica[f(i - 1, j + 1)] : 0))) /
                            matrica[f(i - 1 , 0)];
      EndIf
      j += 1;
    EndWhile
    i += 1;
  EndWhile
  If matrica[f(broj_redaka - 1, 0)] = polinom[stupanj_polinoma] Then
    Return 1;
  EndIf
  Return 0;
EndFunction

Function broj_korijena_u_desnoj_poluravnini() Which Returns Integer16 Does
  Integer16 i := 1, brojac := 0;
  While i < stupanj_polinoma + 1 Loop
    brojac += not(signum(matrica[f(i, 0)]) = signum(matrica[f(i - 1, 0)]));
    i += 1;
  EndWhile
  Return brojac;
EndFunction

Function obrni_polinom() Which Returns Nothing Does
  Decimal64 pomocni_polinom[20];
  Integer16 i := 0, j := stupanj_polinoma;
  While i < stupanj_polinoma + 1 Loop
    pomocni_polinom[i] := polinom[j];
    i += 1;
    j -= 1;
  EndWhile
  i := 0;
  While i < stupanj_polinoma + 1 Loop
    polinom[i] := pomocni_polinom[i];
    i += 1;
  EndWhile
EndFunction

It seems to work so far.

So, we can focus on my second question: How can I solve the preparation for the laboratory exercise that is asking to calculate the range (interval) of gain for which the system will be stable using both the Hurwitz'es Criterion and the Bode's Criterion? Neither the Hurwitz'es Criterion nor the Bode's Criterion give us ranges. Hurwitz'es Criterion gives us the number of poles on the right-hand-side of the imaginary axis, which is always zero for stable systems. Bode's Criterion gives us, for stable systems, the Amplitude Security and Phase Security. Can you somehow calculate the range of gain for which the system is stable using Amplitude Security and Phase Security? I don't know.

If you ping the Hysenberg criterion with a quantum filiment while goosing the Wilhelm Integer through a Vorpal Complexitor, you'll be able to vector the nunning-Brewger Bridge on the 7th rotation.

And, if done correctly, you can also save the life of Kaiser Wilhelm thus preventing WW1.