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Robust state feedback \(H_\infty \) control for uncertain 2-D continuous state delayed systems in the Roesser model

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Abstract

This paper is concerned with the problem of robust state feedback \(H_\infty \) stabilization for a class of uncertain two-dimensional (2-D) continuous state delayed systems. The parameter uncertainties are assumed to be norm-bounded. Firstly, a new delay-dependent sufficient condition for the robust asymptotical stability of uncertain 2-D continuous systems with state delay is developed. Secondly, a sufficient condition for \(H_\infty \) disturbance attenuation performance of the given system is derived. Thirdly, a stabilizing state feedback controller is proposed such that the resulting closed-loop system is robustly asymptotically stable and achieves a prescribed \(H_\infty \) disturbance attenuation level. All results are developed in terms of linear matrix inequalities. Finally, two examples are provided to validate the effectiveness of the proposed method.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61273120 and the Postgraduate Innovation Project of Jiangsu Province (Grant No. CXZZ13_0208).

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  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Imran Ghous & Zhengrong Xiang

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  1. Imran Ghous
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Correspondence to Zhengrong Xiang.

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Ghous, I., Xiang, Z. Robust state feedback \(H_\infty \) control for uncertain 2-D continuous state delayed systems in the Roesser model. Multidim Syst Sign Process 27, 297–319 (2016). https://doi.org/10.1007/s11045-014-0301-8

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