Using the RouthHurwitz criterion determine the stability of

Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system that has the following characteristic equation: S^Y + 10S^2 + 5S + 120 = 0

Solution

In closed loop transfer function:

a₀sⁿ + a₁s^n-1 +...+a_n-1s +a_n =0

S³+10S² +5S+120 =0

a₀ =1, a₁ =10; a₂=5; a₃ =120

S³   a₀    a₂

S²   a₁   a₃

S¹   a₁a₂-a₀a₃/ a₁

S⁰   a₃

_{Therefore the sability is determined by:}

_S³ 1 5

S² 10 120

S¹ -7

S⁰ 120