Ellipsoidal Techniques for Reachability Analysis of Discrete-Time Linear Systems

This paper describes the computation of reach sets for discrete-time linear control systems with time-varying coefficients and ellipsoidal bounds on the controls and initial conditions. The algorithms construct external and internal ellipsoidal approximations that touch the reach set boundary from outside and from inside. Recurrence relations describe the time evolution of these approximations. An essential part of the paper deals with singular discrete-time linear systems.