Practical stabilization of nonlinear/uncertain dynamic systems with bounded controllers

Abstract

We address the problem of practically stabilizing nonlinear and/or uncertain continuous-time dynamic systems when the norm of the control input is subject to a given fixed bound. We consider a class of systems whose nominal part is linear and whose nonlinear/uncertain part does not satisfy the matching condition. In this treatment no statistical information regarding the uncertainties is needed. Only a norm-bound on each nonlinear/uncertain quantity is assumed. We propose a bounded state-feedback controller whose design incorporates elements from both variable structure control theory and the deterministic control methodology. Using the second method of Lyapunov we obtain sliding domains, regions of uniform ultimate boundedness, and estimates of the domain of attraction for systems employing this controller. The closed-loop stability analysis as well as the design of the controller is facilitated by introducing a special coordinate transformation. The approach is illustrated by a numerical example.