Given the characteristic equation:
F(z) = z^3 + z^2 + kz - 0.5 = 0
a) Use the Jury test to determine the range of "k" that ensures the system is BIBO stable. Show any inequality graphs and how they are combined to determine the valid range of k.
b) Validate your answer by checking that the roots of F(z) are inside the unit circle for the endpoints of your solution. This may be done with Matlab