ABSTRACT
We need a technique to ascertain the stability of the closed-loop (CL) system. Generally, this means whether the roots of CL characteristic polynomial (CP) p(z) all lie within the unit circle. This is shown as
p z T z
G z H z
G z H z ( ) ( )
( )
( )
( )
( ) = =
+ denominator of
ˇ
ˇ1
(4.1)
or p z zI K( ) = − +Φ Γ (4.2)
Equation 4.2 is a polynomial in z given by
p z a z a z a a n n
n( ) ( )= + + + =−0 1 1 0 1 generally
This technique should be simple and involve {ai} only and should be applicable to any polynomial in z.
