Synthesis of Regular Controls for the Global CLF Stabilization of Nonlinear Systems *

Our main purpose in this paper is to address the synthesis problem of regular feedback stabilizers for affine systems with compact convex control value sets. Working along the line of Artstein-Sontag's control Lyapunov function (CLF) approach, we study the conditions to attain the global CLF stabilization of systems with generic (compact and strictly convex) control value sets U, and consider a general form of regular feedback control stabilizers u(x) that comprehends most of the proposed control formulae. Further, we design a formula for a one-parameterized family of suboptimal regular feedback controls that globally asymptotically stabilize a system, provided an appropriate CLF is known.