Abstract

A linear stationary system of differential-algebraic equations of an arbitrarily high unsolvability index with interval coefficients is considered. Sufficient conditions under which the general solution of the perturbed system has the same structure as the solution of the original system are obtained. These conditions are formulated as finite relations to be satisfied by the interval coefficients. Under the assumptions that ensure the preservation of the general solution structure, constructive estimates of the quantity determining the range of uncertainty under which the interval family differential-algebraic equations under examination is robustly stable are obtained. In particular, the robust stability conditions are obtained under the assumption that the original system is superstable.

中文翻译：

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一个微分-代数方程的区间族的稳定性

摘要

考虑具有间隔系数的任意高不可溶指数的微分代数方程的线性平稳系统。获得了充分条件，在该条件下，被摄动系统的一般解具有与原始系统的解相同的结构。这些条件被公式化为由间隔系数满足的有限关系。在确保保留一般解结构的假设下，获得了确定量的建设性估计值，在该不确定性范围内，所考察的区间族微分-代数方程是鲁棒稳定的。特别是，在原始系统超稳定的假设下获得了鲁棒的稳定性条件。