LMI–Based Robust Control of Uncertain Nonlinear Systems via Polytopes of Polynomials

Abstract

This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

“…Methodology: The proposal is based on an exact convex rewriting of the uncertain nonlinear system over a compact set 38 and a formulation of the exact discretization as an Euler discrete approximation with norm‐bounded uncertainties; knowledge of the exact discretization, which is not obtainable in general, is thus not required. A robust digital controller is designed in the spirit of Reference 33 for the aforementioned formulation; it is shown that its sampled‐data implementation robustly stabilizes the continuous uncertain nonlinear system.…”