This paper studies a notion of topological entropy for switched systems, formulated in terms of the minimal number of trajectories needed to approximate all trajectories with a finite precision. For general switched linear systems, we prove that the topological entropy is independent of the set of initial states. We construct an upper bound for the topological entropy in terms of an average of the measures of system matrices of individual modes, weighted by their corresponding active times, and a lower bound in terms of an active-time-weighted average of their traces. For switched linear systems with scalar-valued state and those with pairwise commuting matrices, we establish formulae for the topological entropy in terms of active-time-weighted averages of the eigenvalues of system matrices of individual modes. For the more general case with simultaneously triangularizable matrices, we construct upper bounds for the topological entropy that only depend on the eigenvalues, their order in a simultaneous triangularization, and the active times. In each case above, we also establish upper bounds that are more conservative but require less information on the system matrices or on the switching, with their relations illustrated by numerical examples. Stability conditions inspired by the upper bounds for the topological entropy are presented as well.

本文研究了交换系统的拓扑熵的概念，该概念是用以有限的精度近似所有轨迹所需的最小轨迹数来表示的。对于一般的线性开关系统，我们证明了拓扑熵与初始状态集无关。我们根据各个模式的系统矩阵的度量值的平均值（由其相应的活动时间加权）来构造拓扑熵的上限，而根据其迹线的活动时间加权平均值来构建拓扑熵的下限。对于具有标量值状态的交换线性系统和具有成对交换矩阵的线性系统，我们根据各个模式的系统矩阵特征值的有效时间加权平均值，建立了拓扑熵的公式。对于同时三角形化矩阵更一般的情况，我们构造拓扑熵的上限，该上限仅取决于特征值，它们在同时三角形化中的顺序以及激活时间。在上述每种情况下，我们还建立了较为保守的上限，但需要较少的关于系统矩阵或切换的信息，并通过数值示例说明了它们的关系。还介绍了由拓扑熵的上限启发的稳定性条件。我们还建立了较为保守的上限，但需要较少的关于系统矩阵或切换的信息，并通过数值示例说明了它们的关系。还介绍了由拓扑熵的上限启发的稳定性条件。我们还建立了较为保守的上限，但需要较少的关于系统矩阵或切换的信息，并通过数值示例说明了它们之间的关系。还介绍了由拓扑熵的上限启发的稳定性条件。