For the given system, it is desired that the system be stable.

For the given system, it is desired that the system be stable. The minimum value of α for this condition is _________.

From the characteristic equation
1 + G(s) H(s) = 0

1 +	(s + α)	= 0
	s³ + (1 + α)s² + (α - 1)s + (1 - α)

∴ s³ + (1 + α)s² + αs +1 = 0
By Routh Hurwitz criteria
(1 + α) α >1
(α² + α – 1) > 0
∴ α = 0.618 & – 0.618
But for system to be stable
α = 0.618