3406-6-1P AID: 1825 | 12/07/2013
RID: 1759 | 22/07/2013
Consider the characteristic equation,
Apply Routh-Hurwitz criteria for Equation
Figure 1: Routh-Hurwitz diagram
The system is stable if the equation satisfies the following conditions:
• All the terms in the first column of the Routh’s array should have a positive sign.
• The first column of Routh’s array should not posses any sign change.
From the above statement, there are two sign changes from row to row and row to row. In the fifth order given equation, there are two sign changes. So two poles are in right-half plane and remaining three poles are in left-half plane.
Thus, the system is unstable and has right-half plane poles and left-half plane poles.