论文标题
在线性约束切换系统中查找具有高渐近生长速率的矩阵序列
Finding Matrix Sequences with a High Asymptotic Growth Rate for Linear Constrained Switching Systems
论文作者
论文摘要
线性约束开关系统是线性开关系统，其开关序列受确定性有限自动机的约束。这项工作研究了如何生成一系列矩阵，其渐近生长速率接近受约束的关节频谱半径（CJSR），以实现受约束开关系统的约束，这是我们的先前结果，该结果揭示了约束开关系统和举起的任意切换系统的等效性。通过使用方形优化程序的双重解决方案，算法是为提起的任意切换系统设计的，以生成具有渐近生长速率的矩阵序列，该矩阵接近原始约束开关系统的CJSR。还表明，可以将用于任意切换系统设计的现有算法应用于升起的系统，以便可以为约束开关系统生成所需的矩阵序列。提供了几个数值示例，以说明与现有算法相比，提出的算法的性能更好。
Linear constrained switching systems are linear switched systems whose switching sequences are constrained by a deterministic finite automaton. This work investigates how to generate a sequence of matrices with an asymptotic growth rate close to the constrained joint spectral radius (CJSR) for constrained switching systems, based on our previous result that reveals the equivalence of a constrained switching system and a lifted arbitrary switching system. By using the dual solution of a sum-of-squares optimization program, an algorithm is designed for the lifted arbitrary switching system to produce a sequence of matrices with an asymptotic growth rate that is close to the CJSR of the original constrained switching system. It is also shown that a type of existing algorithms designed for arbitrary switching systems can be applied to the lifted system such that the desired sequence of matrices can be generated for the constrained switching system. Several numerical examples are provided to illustrate the better performance of the proposed algorithms compared with existing ones.
