线性周期切换系统的渐近稳定性

为了研究一类线性周期切换系统的全局渐近稳定性问题,基于驻留时间的方法,当切换系统的各子系统均为稳定的情况下,给出了切换周期的最小下界;当切换系统中含有不稳定的子系统,建立了稳定子系统的驻留时间总和与不稳定子系统的驻留时间总和之间的关系：同时当各子系统的驻留时间均等时,得到了切换周期的设计条件。这些充分条件对于判断一类线性周期切换系统的渐近稳定性具有实用性。仿真结果表明所提出的切换方法是有效的。     

Semi-exact Solutions of Konwent Potential

In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).