Stability of Polynomials: Hurwitz-Routh & Nyquist Locus Curve

[sirijo246]

1) As far as i think i understand, stability of a polynomial means; the polynomial correspond to a (its inverse laplace transform) differential equation, and the differential equations solution is dependent on the coefficiants of this polynomial? if the polynomial is unstable the solution of the corresponding differential equation has oscillations increasing towards infinity...?? this is how i understood transferfunctions, but then again we have a fraction of to polynomials and the poles, the roots of the demoninator give the values of the exponential functions power,

but when we just have a polynomial i am not shure what stality means..??


2) the hurwitz-Routh-criterion for stability, is this some kind of shortcut to see weather all the roots have negtive real parts? Or what does it prove about our polynomial?

3) The Nyquist locus curve, i know how to analyze wether the corresponding polynomial is stable, but i don't know a) how it is plotted
b) is it also telling us something about the values of the roots?

Greatful for any replies as i have my advanced mathematics exam on monday!
siri

 

[CEL]

A polynomial is not stable or unstable. Stability is a property of dynamical systems.
If a polynomial represents the denominator of the transfer function of a dynamic system, its roots are the natural frequencies of the system.
If some of the roots have positive real parts, the system is unstable.
The Routh-Hurwitz algorithm allows the determination of the number of roots with positive real parts, without calculating the value of the roots.

 

[sirijo246]

thank you