Overlapping block diagonal dominance and existence of Lyapunov functions (Q1095219)

The main objective of this paper is to formulate a generalization of block diagonal dominance, which can be used to establish nonsingularity of matrices via overlapping diagonal blocks. A number of stability results are derived in the new setting by exploiting the well-known M- matrix properties, as well as extensions of the normalization, scaling, and alternative norm utilization. A link between generalized block diagonal dominance and vector Lyapunov functions is established, which can be applied in the stability analysis of interconnected dynamic systems.