Polytopic discrete-time models for systems with time-varying delays

Abstract

This paper focuses on the modeling of linear systems with time-varying input delays. During the discretization process, three cases can be differentiated with respect to the structure of the continuous-state transition matrix: non-defective with real eigenvalues, non-defective with complex-conjugated eigenvalues and defective matrices with real/complex- conjugated eigenvalues. The goal is to model the variable input delays as a polytopic uncertainty in order to preserve a linear difference inclusion framework. It is shown that the embedding problem can be translated into a polytopic containment problem and an iterative approach to the construction of tight, low complexity embedding (in terms of a simplex body) is proposed. © 2012 Springer-Verlag GmbH Berlin Heidelberg.