Orthotopic and Ellipsoidal Simulations for a Class of Non-Linear Systems

In this paper, we address the problem of propagating in time an orthotopic or ellipsoidal bounding set for the state of discrete-time quadratic systems. The sequence of bounding sets is called the set simulation of the system, and conveys useful information about the stability and other qualitative behaviors of the possible trajectories of the system. The bounding sets are computed recursively via numerically efficient algorithms