  As modern engineering systems grow in complexity, attitudes toward a modular
design approach become increasingly more favorable. A key challenge to a
modular design approach is the certification of robust stability under
uncertainties in the rest of the network. In this paper, we consider the
problem of identifying the parametric region, which guarantees stability of the
connected module in the robust sense under uncertainties. We derive the
conditions under which the robust stability of the connected module is
guaranteed for some values of the design parameters, and present a
sum-of-squares (SOS) optimization-based algorithm to identify such a parametric
region for polynomial systems. Using the example of an inverter-based
microgrid, we show how this parametric region changes with variations in the
level of uncertainties in the network.
