论文标题
稳定线性系统的开关间隔的长度
The length of switching intervals of a stable linear system
论文作者
论文摘要
线性开关系统是一个ODE系统，其与时间有关的矩阵从给定的控制矩阵集中获取值。如果系统所有轨迹趋于每个控制功能均为零，则该系统（渐近）稳定。我们考虑可能取决于模式的限制，以保持系统稳定性的开关间隔。当轨迹的稳定性具有短切换间隔意味着所有轨迹的稳定性时？为了回答这个问题，我们介绍了线性操作员的“切割尾部点”的概念，并通过凸分析工具对其进行了研究。我们减少了Chebyshev型指数多项式的构建问题，为此，我们得出了一种算法并呈现相应的数值结果。
The linear switching system is a system of ODE with the time-dependent matrix taking values from a given control matrix set. The system is (asymptotically) stable if all its trajectories tend to zero for every control function. We consider possible mode-dependent restrictions on the lengths of switching intervals which keeps the stability of the system. When the stability of trajectories with short switching intervals implies the stability of all trajectories? To answer this question we introduce the concept of "cut tail points" of linear operators and study them by the convex analysis tools. We reduce the problem to the construction of Chebyshev-type exponential polynomials, for which we derive an algorithm and present the corresponding numerical results.
