This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points has higher dimensionality than in the full-rank case due to the existence of what we define as singular equilibrium points. Our main goal is to design a state-dependent switching function to ensure global asymptotic stability of a chosen point inside this set with conditions expressed in terms of linear matrix inequalities. For this class of systems, global exponential stability is generally impossible to be guaranteed. Hence, the proposed switching function is shown to ensure global asymptotic and local exponential stability of the desired equilibrium point. The position control and the velocity control with integral action of a dc motor driven by a h-bridge fed via a boost converter are used for validation. This practical application example is composed of eight subsystems, and all possible convex combinations of the dynamic matrices are singular.

本文处理连续时间切换仿射系统的全局稳定问题，这些系统的动态矩阵具有秩亏凸组合。对于这些系统，由于我们定义为奇异平衡点的存在，已知的可达到平衡点集比全秩情况具有更高的维度。我们的主要目标是设计一个状态相关的切换函数来确保全局渐近稳定性用线性矩阵不等式表示的条件在该集合内选择一个点。对于这类系统，一般不可能保证全局指数稳定性。因此，所提出的切换函数被证明可以确保所需平衡点的全局渐近和局部指数稳定性。使用通过升压转换器馈电的 h 桥驱动的直流电机的积分作用的位置控制和速度控制进行验证。本实际应用实例由八个子系统组成，动态矩阵所有可能的凸组合都是奇异的。