论文标题
沿轨迹的离散时间平坦度和线性化
Discrete-time Flatness and Linearization along Trajectories
论文作者
论文摘要
本文研究了非线性时间变化的平面离散时间系统与相应的线性时间变化系统之间的关系，这些系统是通过沿轨迹线性化获得的。它是由连续的时间案例激发的，众所周知，沿轨迹的平坦系统的线性化导致线性变化的系统又是平坦的。由于平整性意味着可控性，因此这是固定度的重要必要条件。在目前的贡献中，这表明这在离散的情况下也是如此：我们证明了线性化系统再次平坦，并且可能的平面输出是通过非线性系统的平面输出的线性化给出的。类似地，通过此平面输出描述线性系统系统变量的参数化的地图与非线性系统相应地图的线性化相吻合。结果通过两个示例说明了结果。
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time case, where it is well-known that the linearization of flat systems along trajectories results in linear time-varying systems which are again flat. Since flatness implies controllability, this constitutes an important verifiable necessary condition for flatness. In the present contribution, it is shown that this is also true in the discrete-time case: We prove that the linearized system is again flat, and that a possible flat output is given by the linearization of a flat output of the nonlinear system. Analogously, the map that describes the parameterization of the system variables of the linear system by this flat output coincides with the linearization of the corresponding map of the nonlinear system. The results are illustrated by two examples.
