论文标题
k征收：理论和应用
k-Contraction: Theory and Applications
论文作者
论文摘要
如果任何两个解决方案以指数率相互接近，则动态系统称为承包系统。更确切地说，动力学以指数速率收缩。该特性意味着高度有序的渐近行为，包括夹带时变的周期矢量场，尤其是时间不变的矢量场的全局渐近稳定性。收缩理论发现了在系统和控制理论中的许多应用，因为存在基于矩阵措施的易于验证足够的条件，从而保证了收缩。 在这里，我们提供了称为K级收缩的收缩理论的几何概括。如果动力学以指数速率合同，则动态系统称为K-级合同。对于K = 1，这将减少到标准收缩。 我们描述了易于根据基质测量值和矢量场雅各布式的KTH添加剂化合物来验证k级合约的足够条件。我们还描述了Muldowney和Li的开创性工作的应用，可以在2阶收缩的框架中解释到系统和控制理论。
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior including entrainment to time-varying periodic vector fields and, in particular, global asymptotic stability for time-invariant vector fields. Contraction theory has found numerous applications in systems and control theory because there exist easy to verify sufficient conditions, based on matrix measures, guaranteeing contraction. Here, we provide a geometric generalization of contraction theory called k-order contraction. A dynamical system is called k-order contractive if the dynamics contracts k-parallelotopes at an exponential rate. For k=1 this reduces to standard contraction. We describe easy to verify sufficient conditions for k-order contractivity based on matrix measures and the kth additive compound of the Jacobian of the vector field. We also describe applications of the seminal work of Muldowney and Li, that can be interpreted in the framework of 2-order contraction, to systems and control theory.
