论文标题
线性系统具有有限开关间隔的稳定性
Stability of linear systems with bounded switching intervals
论文作者
论文摘要
我们解决了线性切换系统的稳定性问题，该系统与模式有关的开关间隔限制。它们的长度可以按照下面的（保证的居住时间）的限制。上限使这个问题与经典案例完全不同：稳定的系统可以由不稳定的矩阵组成，它可能不具有Lyapunov功能等。我们介绍了Lyapunov多功能的概念，具有离散的单调性，这为Lyapunov指数提供了上限。它的存在以及不变规范的存在。紧密的下限是 根据修改后的berger-wang公式获得了可误导的切换法律。基于这些结果，我们开发了一种以任意精度计算Lyapunov指数的方法，并分析其在数值结果中的效率。分析可以取消某些上限的情况。
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this problem quite different from the classical case: a stable system can consist of unstable matrices, it may not possess Lyapunov functions, etc. We introduce the concept of Lyapunov multifunction with discrete monotonicity, which gives upper bounds for the Lyapunov exponent. Its existence as well as the existence of invariant norms are proved. Tight lower bounds are obtained in terms of a modified Berger-Wang formula over periodizable switching laws. Based on those results we develop a method of computation of the Lyapunov exponent with an arbitrary precision and analyse its efficiency in numerical results. The case when some of upper bounds can be cancelled is analysed.
