电磁耦合实验平台系统线缆束的电磁拓扑分析

复杂线缆束系统的电磁耦合分析,随着电磁环境的日趋复杂化,显得越来越困难。而高功率电磁辐射技术的发展,对具有复杂电缆束网络和电子设备的系统,带来了严重的电磁威胁。这从电磁攻击与电磁防护两方面,对复杂线缆束的电磁耦合分析,都提出了更加迫切的需求。由于复杂线缆束网络所涉及的几何空间的边界条件十分复杂,所以很难用时域有限差分(FDTD)或频域有限差分(FDFD)方法求解复杂线缆束网络系统的电磁耦合问题。我们在基于传输线理论,采用拓扑学中将空间按照拓扑结构进行分解的思想,建立了线缆束网络电磁耦合的拓扑模型,得出了计算复杂线缆束网络系统终端耦合电压与电流的计算方法,并给出了仿真计算实例用以验证电磁拓扑法处理线缆网络电磁耦合效应的有效性。     

Lyapunov-barrier characterization of robust reach–avoid–stay specifications for hybrid systems

Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach–avoid–stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be computationally expensive due to the use of state–space discretization. In contrast, Lyapunov methods qualitatively characterize stability and safety properties without any state–space discretization. Recent work on converse Lyapunov-barrier theorems also demonstrates an approximate completeness for verifying reach–avoid–stay specifications of systems modeled by nonlinear differential equations. In this paper, based on the topology of hybrid arcs, we extend the Lyapunov-barrier characterization to more general hybrid systems described by differential and difference inclusions. We show that Lyapunov-barrier functions are not only sufficient to guarantee reach–avoid–stay specifications for well-posed hybrid systems, but also necessary for arbitrarily slightly perturbed systems under mild conditions. Numerical examples are provided to illustrate the main results.