This article provides new conditions for testing the structural stability of 3D Roesser models. The models can be discrete, continuous, or mixed discrete/continuous. The conditions consist in a few tests on the eigenvalues of matrices and one test on an auxiliary 2D model. The latter test is based upon a hierarchy of linear matrix inequalities relaxations. The global test for structural stability is necessary and sufficient for a large enough value of the hierarchy level.

中文翻译：

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3D Roesser 模型稳定性的新测试

本文为测试 3D Roesser 模型的结构稳定性提供了新的条件。模型可以是离散的、连续的或混合离散/连续的。条件包括对矩阵特征值的一些测试和对辅助二维模型的一项测试。后一个测试基于线性矩阵不等式松弛的层次结构。对于足够大的层级值，结构稳定性的全局测试是必要且充分的。