Routh–Hurwitz stability criterion

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This respiratory contains a MATLAB code that includes a main program and RouthCriteria class, this program takes input from user (transfer function) then extract the numerator and denominator polynomials and apply Routh criteria to examine stability.

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In "routh_proj.mlx" user will give the inputs and run the code lines then "RouthCriteria.m" class will be called that carries the logic. Also this analysis carries special cases of routh criteria.

Main logic

for i is row index and p is column index of our routh matrix(table) without appending the new rows

the new row in matrix of index m where m as counter of new rows indecies will have value starts from i and cosiquently will have elements of index (i,p) or (m,p) where index (m,p) carries value equals to values strored in following indecies in our matrix ( ( (i+1,p) * (i,p+1) ) - ( (i,p) * (i+1,p+1))) / (i,p)

As shown in the code

           

           for i=1:itter  %%excute routh criteria , itter is order of charactaristic equation minus 2
               try
                    for p= 1:y
                        
                           mul1=new_rows((i+1),p);
                           mul2=new_rows((i),(p+1));
                           mul3=new_rows((i),(p));
                           mul4=new_rows((i+1),(p+1));
                           num2=(mul1*mul2)-(mul3*mul4);
                           new = num2/new_rows((i+1),p);
                           append_row(i,p)=new;
                           
                    end
               catch
               append_row(i,p)=0;
               end

Output

You can expect output to be routh table and a line that tells whether the system is stable or not and the number of real poles also a graph of the system root locus.

Note that the equation evaluated in following figure is of special case where whole row is zeros