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Global CLF stabilization for systems with compact convex control value sets

In this paper, we address the global stabilization problem for affine systems by means of feedback controls taking values in compact convex control value sets U. Working along the line of Sontag's (1989) control Lyapunov function (CLF) approach, we obtain a one-parameterized family of continuous bounded feedback controllers that globally asymptotically stabilizes a system, provided a CLF is known. We obtain first the global stabilization result for smooth compact and strictly convex control value sets; then, we present a procedure for approximating polytopes that allows us to extend the results to convex control value sets. The designed family of controls is suboptimal with respect to the CLF and set U.