This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of paraboloidal overapproximations. These paraboloids are supported by the reachable tube on touching trajectories. Parameters of each paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.

中文翻译：

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具有积分二次约束的线性时不变系统可达性分析的抛物线组仿真

本文描述了线性时不变系统的可达集和管道的计算，该线性时不变系统的输入未知，其整数二次约束，例如延迟，速率限制器或能量边界的建模。我们定义了抛物面超近似族。这些抛物面由触及轨迹上的可到达管支撑。每个抛物面的参数表示为初始值问题的解决方案。与以前的基于经典线性二次调节器的方法相比，我们的方法也可以应用于不稳定的系统。我们在大型系统上测试了我们的方法。