  The small-signal stability is an integral part of the power system security
analysis. The introduction of renewable source related uncertainties is making
the stability assessment difficult as the equilibrium point is varying rapidly.
This paper focuses on the Differential Algebraic Equation (DAE) formulation of
power systems and bridges the gap between the conventional reduced system and
the original one using logarithmic norm. We propose a sufficient condition for
stability using Bilinear Matrix Inequality and its inner approximation as
Linear Matrix Inequality. Another contribution is the construction of robust
stability regions in state-space in contrast to most existing approaches trying
same in the parameter space. Performance evaluation of the sufficiency
condition and its inner approximation has been given with the necessary and
sufficient condition for a small-scale test case. The paper provides a
necessary base to develop tractable construction techniques for the robust
stability region of power systems.
