Robust stabilization of uncertain nonlinear systems using differential algebraic representations

Abstract

Regional robust stabilization for a class of uncertain MIMO nonlinear systems with parametric uncertainties is investigated. The closed-loop robust stability is achieved using linear timeinvariant state feedback control. In this context, two cases are investigated: (i) uncertain nonlinearsystems resulting from attempts to use the well-known Input-Output Feedback Linearization technique applied considering nominal parameters; and (ii) uncertain nonlinear systems with input saturation. In both cases, the fact that the uncertain systems have Differential AlgebraicRepresentations (DAR) is the main theoretical assumption employed to derive sufficient conditions, in the form of Linear Matrix Inequalities (LMI), to solve the corresponding control problem. The regional character of the stability result obtained using this approach is associated with the largest ellipsoidal Domain of Attraction (DOA), considered to be inside a given polytopic region in the closed-loop system state space, which is a byproduct of solving the associated optimization problem of searching for appropriate feedback gain matrices. Specifically, the thesiscontributions are new sufficient LMI conditions with new decision variables used to compute the feedback gain matrices without prior knowledge of an initial stabilizing matrix. The new conditions have also shown favorable comparisons with recently published similar control design methodologies, particularly for the case of uncertain nonlinear systems with input saturation, where a polytopic description of this nonlinearity has led to new LMI conditions.