Exact recursive updating of uncertainty sets

Abstract: This paper addresses the classical problem of determining the set of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present two theorems which describe completely how they evolve with time, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.