Due to their relevance in systems analysis and (robust) controller design, we consider the problem of determining control-theoretic system properties of an a priori unknown system from data only. More specifically, we introduce a necessary and sufficient condition for a discrete-time linear time-invariant system to satisfy a given integral quadratic constraint (IQC) over a finite time horizon using only one input–output trajectory of finite length. Furthermore, for certain classes of IQCs, we provide convex optimization problems in form of semidefinite programs (SDPs) to retrieve the optimal, i.e. the tightest, system property description that is satisfied by the unknown system. Finally, we provide bounds on the difference between finite and infinite horizon IQCs and illustrate the effectiveness of the proposed scheme in a variety of simulation studies including noisy measurements and a high dimensional system.

由于它们在系统分析和（稳健的）控制器设计中的相关性，我们考虑仅从数据确定先验未知系统的控制理论系统特性的问题。更具体地说，我们为离散时间线性时不变系统引入了一个必要和充分条件，以仅使用一个有限长度的输入-输出轨迹在有限时间范围内满足给定的积分二次约束 (IQC)。此外，对于某些类别的 IQC，我们提供以半定程序 (SDP) 形式出现的凸优化问题，以检索未知系统所满足的最优，即最紧密的系统属性描述。最后，我们提供了有限和无限水平 IQC 之间差异的界限，并说明了所提出方案在各种模拟研究中的有效性，包括噪声测量和高维系统。