论文标题
稳定等级不足的连续时间开关仿射系统
Stabilization of rank-deficient continuous-time switched affine systems
论文作者
论文摘要
本文处理了连续时期切换仿期系统的全球稳定问题，这些仿期系统具有缺陷的动态矩阵组合。对于这些系统，由于我们将其定义为奇异平衡点的存在，因此已经知道的一组可达到的平衡点具有比全等级情况更高的维度。我们的主要目标是设计一个依赖状态的切换函数，以确保该集合中所选点的全局渐近稳定性，并用线性矩阵不平等表示的条件。对于这类系统，通常无法保证全球指数稳定性。因此，提出的开关函数被证明可确保所需平衡点的全局渐近和局部指数稳定性。通过升压转换器驱动的H桥驱动的直流电动机的积分动作的位置控制和速度控制用于验证。这个实用的应用示例由八个子系统组成，动态矩阵的所有可能的凸组合都是单数。
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 an 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.
