Nonlinear stabilization with bounded controller

This In this paper, an extension of the Sontag´s universal formula is proposed. For benchmark, the proposed method is compared with two other approaches, i.e. a universal Sontag´s formula and a direct Lyapunov with comparing square. To observe the efficacy of the proposed method, a numerical nonlinear system with cubic damping is stabilized. The effectiveness of the proposed method is shown that the magnitude of the control signal can be bounded without a catastrophic effect to the closed loop stability. Other appealing features of the proposed method is that the stabilization cost can be reduced, and the elimination of the useful nonlinear terms can be avoided.