AI 中文总结
本文梳理MIMO有限维线性时不变系统的相关成果，改进无理SISO传递函数的跟踪问题，给出多项式系数热方程的应用实例，完善了此类系统输入输出映射的描述方法。
AI 中文摘要
本文研究多输入多输出（MIMO）有限维线性时不变系统及无理单输入单输出（SISO）传递函数，两类问题均旨在尽可能清晰地描述输入-输出映射$u(\cdot) \to y(\cdot)$的取值范围。有限维系统的相关理论较为完善但成果稀少，本文首要目标是全面梳理该方向的主要结果；其次是改进近期关于无理SISO传递函数跟踪问题的成果，使其能完整描述输入$u \in L^2(0,\times)$下此类系统的输出，文中还给出了多项式系数热方程的应用实例。
英文摘要
In this paper we consider (MIMO) finite dimensional linear and time-invariant systems and irrational single-input single-output (SISO) transfer functions. In both cases our aim is to describe as best as possible the range of the input-output map $u(\cdot) \mapsto y(\cdot)$. The theory in finite dimension is quite satisfying but rather scarce, the first aim of this paper is to collect the main results in this direction in a comprehensive way. Our second aim is to improve a recent result on the tracking problem for irrational SISO transfer functions, allowing one to completely describe the outputs of such system for inputs $u \in L^2(0,\infty)$. An application is given for a heat equation with polynomial coefficients.
