Parabolic set simulation for reachability analysis of linear time-invariant systems with integral quadratic constraint

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 paraboloidal overapproximations. These paraboloids are supported tube on touching trajectories. Parameters each paraboloid expressed as solution to initial value problem. Compared previous methods based classical regulator, our approach can be applied unstable well. tested large scale systems.