We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. https://doi.org/10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

中文翻译：

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微分代数系统通常是可控制和稳定的

我们研究线性，时不变的微分代数系统的各种可控性和稳定性概念的通用性。基于这些概念的众所周知的代数表征（请参阅Berger和Reis的调查文章（在：Ilchmann A，Reis T（eds）中）微分代数方程组I的测量，微分代数方程组论坛，施普林格，柏林，第1页–61。https://doi.org/10.1007/978-3-642-34928-7_1）），我们使用代数几何中的工具以矩阵格式来描述可控制性和稳定性的一般性。