Stabilization of Uncertain Control Systems through Piecewise Constant Feedback

Abstract

This paper investigates the problem of stabilization of nonlinear systems submitted to a deterministic disturbance known by its bounds. The stabilization property is considered in terms of exponential decay of a Lyapunov-like function. As such systems cannot be stabilized by continuous state feedback laws, we consider an approximate stabilization problem with finite horizon. The main result of the paper is the existence of a—discontinuous—piecewise constant feedback control law, achieving the approximate stabilization property. Moreover, in deriving explicitly this feedback law, we show that the number of discontinuity jumps can be related to both precision of the approximate stabilization and time horizon of the control problem considered.