Exponential Stabilization of SISO Nonlinear Systems with Uncertainties

Abstract

The problem of robust stabilization of uncertain single-input and single-output (SISO) nonlinear systems is considered. Based on Lyapunov methods in conjunction with input/output linearization approach, a new approach is proposed to designing a class of continuous and bounded state feedback controllers using the possible bound of the uncertainty for uncertain nonlinear systems. It is shown that the state feedback controller developed in this paper can guarantee exponential stability instead of uniform ultimate boundedness for the nonlinear systems with uncertainties. Because of its continuity, our continuous controller can guarantee the existence of the solution to the dynamical system in usual sense. Moreover, we can easily select the control parameters, so that the method can be expected to have a better transient response. Finally, a numerical example is presented to demonstrate the effectiveness of the approach developed in this paper.