On the Global CLF Stabilization of Systems with Polytopic Control Value Sets

Abstract Our main purpose in this paper is to address the problem of the global asymptotic stabilization of affine systems with control value sets given by polytopes U with 0 ∈ int U . An important polytope is the m -dimensional hyperbox U =[-r − 1 , r + 1 ]×…×[-r − m , r + m ], with -r ± m > 0. Working along the line of Artstein-Sontag's control Lyapunov function (CLF) approach, we study the conditions that a feedback control of the form u ( x ) = ( u 1 ,…, u m ), with uj(x) = ϕj(x)w j (x), should satisfy in order to be admissible (continuous and taking its values in a polytope U ) and globally asymptotically stabilize a system, provided an appropriate CLF is known.