1.

Given the characteristic equation,a(s) = S6 + 4S5 + 3S4 + 2S3 + S + 4S + 4Is the system described by this characteristic equation stable?

Answer»

• All the coefficients are positive and nonzero 

• Therefore, the system satisfies the necessary condition for stability 

• We should determine whether any of the coefficients of the first column of the Routh array are negative

S6 :    1     3    1     4 

S5 :    4     2    4    0 

S4 :    2.5    0    4 

S3 :    2    ‐2.4   0 

S2 :    3     4        

S1 :   ‐1.6    0 

S0 :    4

The elements of the 1st column are not all positive. Then the system is unstable.



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