So my question is basically summarized in the title.
The root of the question lies actually in application of the rules. Namely the stability of linear time invariant feedback systems is determined by concluding that all the the poles of rational polynomial function have negative real parts.
Now in control theory this is very cubersomly solved by use of Hurwitz determinants and constructing wierd tables with loads of special cases. All of this if founded on Routh-Hurwitz theorem.
My question is if there are any more elegant methods to determine any of following :
- Number of roots with negative real parts
- Number of roots with positive real parts
- Ascertain existence of roots with positive real parts ( as to say system is unstable ) ?
- Exclude the possibility that roots with negative/positive real parts exist?