Abstract

We consider an interval family of differential-algebraic equations (DAE) under assumptions that guarantee the coincidence of the structure of the general solution of each of the systems in this family with the structure of the general solution of the nominal system. The analysis is based on transforming the interval family of DAE to a form in which the differential and algebraic parts are separated. This transformation includes the inversion of an interval matrix. An estimate for the stability radius is found assuming the superstability of the differential subsystem of nominal DAE. Sufficient conditions for the robust stability are obtained based on the superstability condition for the differential part of the interval family.

中文翻译：

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一类微分-代数方程的区间族的超稳定性

摘要

我们在保证该系列中每个系统的一般解的结构与名义系统的一般解的结构一致的假设下考虑一个微分-代数方程（DAE）的区间族。该分析基于将DAE的区间族转换为微分部分和代数部分分开的形式。该变换包括间隔矩阵的求逆。假设标称DAE的差分子系统具有超稳定性，则可以找到稳定半径的估计值。基于区间族微分部分的超稳定性条件，可以获得鲁棒稳定性的充分条件。