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Model following control for continuous-time discrete-valued input systems

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Abstract

This paper considers a model following control problem for continuous-time discrete-valued input systems, i.e., systems including the signal quantization such as networked control systems. The constraints we address is the quantized accuracy and switching speed of the signal quantization. This paper considers the two constraints simultaneously, while most of the existing results consider them separately or either of them. Our analysis and synthesis conditions are derived in terms of invariant set and BIBO stability. Especially, the synthesis condition is recast as a set of matrix inequalities based on a non-common Lyapunov variable technique of linear matrix inequality-based multi-objective control. Moreover, we clarify the effectiveness of the proposed method through a numerical example.

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Notes

  1. (20) is the dual inequality of the standard Lyapunov inequality \(\Gamma (h)^{\text {T}}\mathcal{Q}\Gamma (h)-\mathcal{Q}<0\) where \(0<\mathcal{Q}\in \mathrm{I\!R}^{2 n_p\times 2 n_p}\)[15]. This paper uses (20) in order to simplify the derivation of controller synthesis conditions.

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Acknowledgments

We would like to thank the reviewers for their valuable comments. This work was partly supported by JSPS KAKENHI Grant Number 24760332 and 26420429.

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Authors and Affiliations

  1. Graduate School of Informatics and Engineering, The University of Electro-Communications, 1–5–1 Chofugaoka, Chofu, Japan

    Kenji Sawada & Seiichi Shin

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  1. Kenji Sawada
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  2. Seiichi Shin
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Correspondence to Kenji Sawada.

Additional information

This work was presented in part at the 19th International Symposium on Artificial Life and Robotics, Beppu, Oita, January 22–24, 2014.

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Sawada, K., Shin, S. Model following control for continuous-time discrete-valued input systems. Artif Life Robotics 19, 277–285 (2014). https://doi.org/10.1007/s10015-014-0169-6

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