Set simulations for quadratic systems

In this paper, we study the problem of propagating in time a bounding set for the state of a class of nonlinear quadratic systems. The sequence of bounding sets is called the set simulation of the system, and conveys useful information about the stability and qualitative behavior of the possible time responses of the system. Numerically, efficient recursive algorithms are presented for the specific cases when the bounding sets are orthotopes or ellipsoids.