## 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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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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DOI: https://doi.org/10.1007/s11045-014-0301-8

### Keywords

- 2-D continuous systems
- Time-varying delays
- State feedback
- \(H_\infty \) performance
- Roesser model
- Robust stability