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$$H_\infty $$ Control and $$\varepsilon $$ -Bound Estimation of Discrete-Time Singularly Perturbed Systems | Circuits, Systems, and Signal Processing Skip to main content
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\(H_\infty \) Control and \(\varepsilon \)-Bound Estimation of Discrete-Time Singularly Perturbed Systems

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Abstract

This paper considers the problems of \(H_\infty \) control and \(\varepsilon \)-bound estimation of discrete-time singularly perturbed systems. A set of well-defined conditions for the existence of state feedback controllers are proposed, under which the resulting closed-loop system is asymptotically stable while satisfying a prescribed \(H_\infty \) norm bound when the singular perturbation parameter \(\varepsilon \) is lower than a pre-defined upper bound. It is shown that the proposed controller design method is less conservative than the existing ones. Furthermore, a method of estimating the \(\varepsilon \)-bound is proposed, which leads to less conservative results and requires lower computational burden than the existing methods for a wide class of singularly perturbed systems. Finally, examples are given to show the advantages and effectiveness of the obtained results.

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Authors and Affiliations

  1. School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Chunyu Yang & Linna Zhou

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  1. Chunyu Yang
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  2. Linna Zhou
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Correspondence to Chunyu Yang.

Additional information

This work was supported by the National Natural Science Foundation of China (61374043), the Jiangsu Provincial Natural Science Foundation of China (BK20130205), the China Postdoctoral Science Foundation funded project (2013M530278, 2014T70558), the Fundamental Research Funds for the Central Universities (2013QNA50, 2013RC10, 2013RC12, 2013XK09) and the Natural Science Foundation of Liaoning Province (201202201). The original and a shortened version of this work was presented at the 28th youth academic conference of Chinese Association of Automation, April 26–28, 2013, Hefei, China.

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Yang, C., Zhou, L. \(H_\infty \) Control and \(\varepsilon \)-Bound Estimation of Discrete-Time Singularly Perturbed Systems. Circuits Syst Signal Process 35, 2640–2654 (2016). https://doi.org/10.1007/s00034-015-0165-7

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