A linear multi-agent systems approach to diffusively coupled piecewise affine systems: Delay robustness

In this paper, we investigate ultimate boundedness of large-scale arrays consisting of piecewise affine (PWA) sub-systems linearly interconnected through channels with delays. Under an assumption on subsystem dynamics, it is shown that ultimate boundedness can be reduced to the stability of a linear delay differential system. This enables us to use linear multi-agent system theory. As a result, we obtain sufficient conditions for ultimate boundedness taking the robustness of the interconnection topology into account. The usefulness of the results is examined through its application to the FitzHugh-Nagumo model.