On the Stability and Estimation of Ultimate Boundedness of Nonlinear/Uncertain Dynamic Systems with Bounded Controllers

This paper addresses the problem of stabilization of a class of uncertain and/or nonlinear dynamic systems for which matching conditions are not satisfied. No statistical description of uncertain elements is assumed. The uncertain and/or nonlinear quantities are described only in terms of bounds and their possible sizes. A stabilizing bounded controller is proposed whose design utilizes elements of the variable structure control theory. Regions of uniform ultimate boundedness (practical stability) for systems driven by this bounded controller are estimated. A special coordinate transformation is utilized during the analysis. Sliding domains and estimates of the domain of attraction are obtained with the aid of the Lyapunov method.