Linear systems with conical constraints and convex Lyapunov functions in the framework of convex processes

Linear control systems with conical constraints on controls and on states are modeled by set-valued mappings called convex processes. Asymptotic stability properties of convex processes are described by convex Lyapunov functions. Convex conjugacy of Lyapunov functions is used to show the relationship between asymptotic stability properties of a convex process and of its adjoint/dual process. Implications for asymptotic controllability of a linear system with conical control constraints and for detectability of a dual system are stated.