In (Euzébio et al., 2016 [10]; Chen and Tang, 2020 [8]), the bifurcation diagram and all global phase portraits of a degenerate planar piecewise linear differential system $\dot{x}=F(x)-y,\dot{y}=g(x)-\alpha$ with three zones were given completely for the non-extreme case. In this paper we deal with the system for the extreme case and find new nonlinear phenomena of bifurcation for this planar piecewise linear system, i.e., a generalized degenerate Hopf bifurcation occurs for points at infinity. Moreover, the bifurcation diagram and all global phase portraits in the Poincaré disc are obtained, presenting scabbard bifurcation curves, grazing bifurcation curves for limit cycles, generalized supercritical (or subcritical) Hopf bifurcation curve for points at infinity, generalized degenerate Hopf bifurcation value for points at infinity and double limit cycle bifurcation curve.

在（Euzébio et al., 2016 [10]; Chen and Tang, 2020 [8]）中，退化平面分段线性微分系统的分岔图和所有全局相图 $\dot{X}=F(X)-是,\dot{是}=G(X)-\alpha$对于非极端情况，完全给出了三个区域。在本文中，我们处理极端情况下的系统，并为该平面分段线性系统找到新的分岔非线性现象，即，对于无穷远处的点会发生广义退化 Hopf 分岔。此外，获得了庞加莱圆盘中的分岔图和所有全局相图，给出了刀鞘分岔曲线、极限循环的掠掠分岔曲线、无穷远点的广义超临界（或亚临界）Hopf分岔曲线、点的广义简并Hopf分岔值在无穷大和双极限循环分岔曲线。