  Neural networks have gained popularity in controller design due to their
versatility and efficiency, but their integration into feedback systems can
compromise stability, especially in the presence of uncertainties. This paper
addresses the challenge of certifying robust stability in neural feedback
systems with interval matrix uncertainties. By leveraging classic robust
stability techniques and the recent quadratic constraint-based method to
abstract the input-output relationship imposed by neural networks, we present
novel robust stability certificates that are formulated in the form of linear
matrix inequalities. Three relaxed sufficient conditions are introduced to
mitigate computational complexity. The equivalence of these conditions in terms
of feasibility, as well as their connections with existing robust stability
results, are also established. The proposed method is demonstrated by two
numerical examples.
