Suppose the system has 4 th order characteristic polynomial. Out of four roots, two specific roots will changes the signs (instability, positive real part) with varying the system parameters and other two roots will always shows the stability (-ve real part). Is it right to modify system characteristic equation by taking those roots participating in instability in order to get functional relationship (shows the occurrence of instability) using Routh-Hurwitz criteria in terms of roots coefficient ?.
Can you please restructure your question to make it clearer? I believe the correct word in the first line is 'right' and not 'write'. Sandeep Kumar
Dear Sandeep Kumar ,
The best choice in your case is to do the following:
(1) Write the companion matrix of the characteristic equation.
(2) Use the Gershgorin circle theorem to trap the eigenvalues in discs.
(3) Study the stability of the system according to the location of the eigenvalues.
Best regards
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