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引用次数: 0
摘要
本研究继承了 Ilchmann 和 Kirchhoff (Math Control Signals Syst 33:359-377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann 和 Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) 关于非结构化线性微分代数系统（相对）通用可控性的研究，以及 Ilchmann 等人 (Port-Hamiltonian descriptor systems are generically controllable and stabilizable.提交给《控制、信号和系统数学》（Mathematics of Control, Signals and Systems），2023。https://arxiv.org/abs/2302.05156）关于端口-哈密尔顿描述符系统（相对）通用可控性的研究。我们将他们的结果扩展到可观测性的（相对）通用性。对于非结构微分代数系统，Ilchmann 和 Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) 使用对偶性推导出了（相对）通用可观测性标准。这对于端口-哈密尔顿系统是不可能的。因此，我们调整了 Ilchmann 等人的结果（端口-哈密尔顿描述子系统是一般可控和可稳定的。提交给《控制、信号和系统数学》，2023 年。https://arxiv.org/abs/2302.05156），并推导出与非结构化情况类似的标准。此外，我们还考虑了系统矩阵的某些秩约束。
Generic observability for port-Hamiltonian descriptor systems
The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.
期刊介绍：
Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing.
Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations.
Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.
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