Abstract
This paper investigates the problem of robust \(H_\infty \) repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with \(H_\infty \) performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate 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, the Postgraduate Innovation Project of Jiangsu Province (Grant No. CXZZ13_0208), and the Jiangsu Scientific and Technological Support Plan (Grant No. BE2012175).
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Shao, Z., Huang, S. & Xiang, Z. Robust \(H_\infty \) Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay. Circuits Syst Signal Process 34, 1363–1377 (2015). https://doi.org/10.1007/s00034-014-9905-3
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DOI: https://doi.org/10.1007/s00034-014-9905-3