  New methods for $D$-decomposition analysis are presented. They are based on
topology of real algebraic varieties and computational real algebraic geometry.
The estimate of number of root invariant regions for polynomial parametric
families of polynomial and matrices is given. For the case of two parametric
family more sharp estimate is proven. Theoretic results are supported by
various numerical simulations that show higher precision of presented methods
with respect to traditional ones. The presented methods are inherently global
and could be applied for studying $D$-decomposition for the space of parameters
as a whole instead of some prescribed regions. For symbolic computations the
Maple v.14 software and its package RegularChains are used.
