论文标题
基于近似离散时间模型的采样数据系统的半球体指数输入到状态的稳定性
Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models
论文作者
论文摘要
非线性系统的确切离散时间模型很难或不可能获得，因此可以使用近似模型进行控制设计。大多数现有结果提供了条件，在闭环中，近似模型的稳定性延续到了（未知）精确模型的稳定性，但仅在实际意义上，即闭环系统的轨迹可以确保可以通过限制最大采样期来使其大小可按所需的尺寸缩小，以使其大小可以使其大小。此外，确切模型存在一些非常严格的条件，以表现出与近似模型完全相同的渐近稳定性。在这种情况下，我们的主要贡献包括通过考虑半球体指数输入到状态稳定性（SE-ISS）来提供较少严格的条件，在该指数中，输入可以成功地表示状态测量和驱动错误。这些条件基于建立适当近似模型的SE-IS，并且适用于均匀和非均匀采样。作为第二个贡献，我们表明明确的runge-kutta模型满足了我们的条件，因此可以使用。还给出了基于近似离散时间模型稳定的控制设计的示例。
Exact discrete-time models of nonlinear systems are difficult or impossible to obtain, and hence approximate models may be employed for control design. Most existing results provide conditions under which the stability of the approximate model in closed-loop carries over to the stability of the (unknown) exact model but only in a practical sense, i.e. the trajectories of the closed-loop system are ensured to converge to a bounded region whose size can be made as small as desired by limiting the maximum sampling period. In addition, some very stringent conditions exist for the exact model to exhibit exactly the same type of asymptotic stability as the approximate model. In this context, our main contribution consists in providing less stringent conditions by considering semiglobal exponential input-to-state stability (SE-ISS), where the inputs can successfully represent state-measurement and actuation errors. These conditions are based on establishing SE-ISS for an adequate approximate model and are applicable both under uniform and nonuniform sampling. As a second contribution, we show that explicit Runge-Kutta models satisfy our conditions and can hence be employed. An example of control design for stabilization based on approximate discrete-time models is also given.
