Outer ellipsoidal approximations of the reachable set at infinity for linear systems

Outer ellipsoidal approximations to the reachable set at infinity for a linear control system with bounded scalar controls are obtained using a new method based on quadratic Lyapunov functions. These outer approximations are compared with those given by an algorithm due to Sabin and Summers, and also with certain tangential outer approximations, obtained using a fixed-point iteration scheme.This research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors gratefully acknowledge the assistance of Mr. Ryan Davies, recipient of an NSERC Undergraduate Research Award.