On reachability and null-controllability of nonstrict convex processes

TL;DR

This paper investigates the conditions under which linear discrete-time systems with convex constraints can be controlled to reach desired states or null states, using a geometric framework and spectral analysis of dual processes.

Contribution

It introduces a geometric approach based on invariance properties and provides necessary and sufficient spectral conditions for reachability and null-controllability of convex process systems.

Findings

Established geometric invariance conditions for convex processes.

Derived spectral criteria for controllability and reachability.

Applicable to systems with convex cone constraints.

Abstract

This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are constrained to lie within a convex cone. After developing a geometric framework for convex processes relying on invariance properties, we provide necessary and sufficient conditions for both reachability and null-controllability in terms of the spectrum of dual processes.