Circuits, Systems, and Signal Processing

, Volume 35, Issue 5, pp 1579–1592 | Cite as

Analysis and Design of \(H_{\infty }\) Controllers for 2D Singular Systems with Delays

  • Said Kririm
  • Abdelaziz Hmamed
  • Fernando TadeoEmail author


The \(H_{\infty }\) control design problem is solved for the class of 2D discrete singular systems with delays. More precisely, the problem addressed is the design of state-feedback controllers such that the acceptability, internal stability and causality of the resulting closed-loop system are guaranteed, while a prescribed \(H_\infty \) performance level is simultaneously fulfilled. By establishing a novel version of the bounded real lemma, a linear matrix inequality condition is derived for the existence of these \(H_\infty \) controllers. They can then be designed by solving an iterative algorithm based on LMI optimizations. An illustrative example shows the applicability of the algorithm proposed.


Two-dimensional systems Systems with delays \(H_{\infty }\) control Singular systems 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Sciences Dhar El MehrazUniversity of Sidi Mohamed Ben AbdellahFes-AtlasMorocco
  2. 2.Department Ingenieria de Sistemas y AutomaticaUniversidad de ValladolidValladolidSpain

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