## Abstract

This paper is concerned with the problem of state feedback \(H_\infty \) stabilization of discrete two-dimensional switched delay systems with actuator saturation represented by the second Fornasini and Marchesini state-space model. Firstly, the saturation behavior is described with the help of the convex hull representation, and a sufficient condition for asymptotical stability of the closed-loop system is proposed in terms of linear matrix inequalities via the multiple Lyapunov functional approach. Then, a state feedback controller is designed to guarantee the \(H_\infty \) disturbance attenuation level of the corresponding closed-loop system. Finally, two examples are provided to validate the proposed results.

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## Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61273120, the Postgraduate Innovation Project of Jiangsu Province (Grant Nos. CXZZ13_0208, KYLX_0378), the Jiangsu Scientific and Technological Support Plan (Grant No. BE2012175), the Jiangsu Province “333Project” (Grant No. BRA2012163) and the Visiting Scholar Foundation of Key Lab in University under Grant No. GZKF-201203. The authors would like to thank the Editor-in-Chief, Dr. M.N.S. Swamy, for his helpful comments in improving the presentation of the paper.

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Ghous, I., Xiang, Z. & Karimi, H.R. State Feedback \(H_\infty \) Control For 2-D Switched Delay Systems with Actuator Saturation in the Second FM Model.
*Circuits Syst Signal Process* **34**, 2167–2192 (2015). https://doi.org/10.1007/s00034-014-9960-9

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DOI: https://doi.org/10.1007/s00034-014-9960-9

### Keywords

- Switched systems
- 2-D systems
- Multiple Lyapunov functional
- Asymptotical stability
- \(H_\infty \) performance
- Actuator saturation