Global CLF stabilization of systems with polytopic CVS containing 0 in their boundaries, and positive controls

Our main aim in this work is to study the problem of the global asymptotic stabilization (GAS) of affine control systems with control value sets (CVS) given by (convex) polytopes U with 0 ϵ U, hence allowing 0 in the boundary of U, 0 ϵ ∂U, e.g. positive control inputs. Working along the line of Artstein-Sontag´s control Lyapunov function (CLF) approach, we study the conditions that feedback controls of the decentralized form u(x) = (u₁,..., u_m), with Uj(x) = ρ_j(x)ω_j(x), should satisfy in order to be admissible (regular and valued in a CVS U) and render a system GAS, provided an appropriate CLF is known.