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Strong Structural Controllability and Observability of Linear Time-Varying Systems

机译：线性时变系统的强大结构可控性和可观察性

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摘要

In this note we consider continuous-time systems , as well as discrete-time systems , whose coefficient matrices , , and are not exactly known. More precisely, all that is known about the systems is their nonzero pattern, i.e., the locations of the nonzero entries in the coefficient matrices. We characterize the patterns that guarantee controllability and observability, respectively, for all choices of nonzero time functions at the matrix positions defined by the pattern, which extends a result by Mayeda and Yamada for time-invariant systems. As it turns out, the conditions on the patterns for time-invariant and for time-varying discrete-time systems coincide, provided that the underlying time interval is sufficiently long. In contrast, the conditions for time-varying continuous-time systems are more restrictive than in the time-invariant case.
机译：在本说明中，我们考虑连续时间系统以及离散时间系统，其系数矩阵，和尚不完全清楚。更准确地说，关于系统的所有已知信息都是它们的非零模式，即系数矩阵中非零条目的位置。我们对模式定义的矩阵位置上所有非零时间函数的选择分别描述了可控制性和可观察性的模式，这扩展了Mayeda和Yamada对时不变系统的结果。事实证明，只要基本时间间隔足够长，时不变和时变离散时间系统的模式条件就会重合。相反，时变连续时间系统的条件比时不变情况下的条件更为严格。

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