时变系统的无记忆输出零化和标准型
Memoryless output nullification and canonical forms, for time varying systems
摘要：
研究了无记忆输出反馈消除时变系统的可能性。我们研究的系统是线性单输入单输出有限维时变系统。对于一般的完全可控和完全可观的离散时间系统，我们证明了任何状态在任何时候都可以在有限时间内被引导到原点。一个算法的无效和无效时间的上界，只依赖于系统的尺寸，提供。该算法描述了使用时变控制器规范形式的系统的表示。我们证明，每一个完全可控的系统有这样的表示。的应用程序的无效算法采样数据系统进行了分析：我们表明，一个可控的连续时间时变系统的解析系数，可以利用零保持采样的输出和随时间变化的无记忆线性反馈无效;对于一般的可观的，几乎任何采样周期可以使用。我们还证明了具有解析系数的时变系统的能控性在几乎任何速率的零保持采样下都是保持的。
英文摘要：
We study the possibility of nullifying time-varying systems with memoryless output feedback. The systems we examine are linear single-input single-output finite-dimensional time-varying systems. For generic completely controllable and completely observable discrete-time systems, we show that any state at any time can be steered to the origin within finite time. An algorithm for nullification and an upper bound for nullification time, depending only on the system's dimension, are provided. The algorithm is described using a representation of the system in time-varying controller canonical form. We verify that every completely controllable system has such a representation. The application of the nullification algorithm to sampled-data systems is also analysed: we show that a controllable continuous-time time-varying system with analytic coefficients can be nullified utilising zero-hold sampling of the output and time-varying memoryless linear feedback; for generic observables, almost any sampling period can be used. We also prove that controllability of time-varying systems with analytic coefficients is preserved under zero-hold sampling at almost any rate.
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