Overlapping block diagonal dominance and existence of Liapunov functions

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 Liapunov functions is established, which can be applied in the stability analysis of interconnected dynamic systems.