Comparison of Overapproximation

The presence of a communication network in a control loop induces many imperfections such as varying transmission delays, varying sampling/transmission intervals and packet loss, which can degrade the control performance significantly and can even lead to instability. Various techniques have been proposed in the literature for stability analysis and controller design for these so-called networked control systems (NCSs). The goal of this paper is to survey a particular class of techniques using discrete-time models that are based on polytopic overapproximations of the uncertain NCS model and lead to stability conditions in terms of linear matrix inequalities (LMIs). We discuss the advantages and disadvantages of the existing techniques in both qualitative and quantitative manners. In particular, we apply all methods to a benchmark example providing a numerical comparison of the methods with respect to conservatism as well as numerical complexity. ∗Maurice Heemels, Nathan van de Wouw and Tijs Donkers are supported by the European Community through the FP7-ICT-2007-2 thematic programme under the WIDE224168 project. Jamal Daafouz is supported by the ANR project ArHyCo, ARPEGE, number ANR-2008 SEGI 004. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. HSCC’10, April 12–15, 2010, Stockholm, Sweden. Copyright 2010 ACM 978-1-60558-955-8/10/04 ...$10.00.