This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal recovery results relative to such approximability models, we construct some optimal algorithms and characterize the optimal performance for the identification and evaluation of transfer functions in the framework of the Hardy Hilbert space and of the disk algebra. In particular, we determine explicitly the optimal recovery performance for frequency measurements taken at equispaced points on an inner circle or on the torus.

本文考虑了通过对传递函数进行线性测量来观测到的稳定线性时不变系统的最佳恢复问题。通用的建模假设在这里被相关的假设所代替，即传递函数属于由近似能力描述的模型集。利用相对于此类近似模型的最新最佳恢复结果，我们构造了一些最佳算法，并在Hardy Hilbert空间和磁盘代数的框架内，表征了用于识别和评估传递函数的最佳性能。特别是，我们明确地确定了在内圈或圆环上等距点进行频率测量的最佳恢复性能。