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Input-output finite-time stability of time-varying linear singular systems

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Abstract

This paper studies the input-output finite-time stabilization problem for time-varying linear singular systems. The output and the input refer to the controlled output and the disturbance input, respectively. Two classes of disturbance inputs are considered, which belong to L-two and L-infinity. Sufficient conditions are firstly provided which guarantee the input-output finite-time stability. Based on this, state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable. The conditions are presented in terms of differential linear matrix inequalities. Finally, an example is presented to show the validity of the proposed results.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan Shandong, 250100, China

    Juan Yao, Jun-e Feng, Lin Sun & Yu Zheng

Authors
  1. Juan Yao
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  2. Jun-e Feng
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  3. Lin Sun
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  4. Yu Zheng
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Corresponding author

Correspondence to Juan Yao.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 60974137, 61174141, 61004005, 61074070), the Research Awards Fund for Outstanding Young and Middle-Aged Scientists of Shandong Province (Nos. BS2011SF009, BS2011DX019), and the Independent Innovation Foundation of Shandong University (Nos. IIFSDU2009TS085, 2010TS007).

Juan YAO received her M.S. degree from Shandong University in 2011. Her research interests include descriptor systems and semitensor product.

Jun-e FENG received her Ph.D. degree from Shandong University in 2003. Since 2009, she has been a professor with the School of Mathematics, Shandong University. Her research interests include descriptor systems, time-delay systems and semitensor product.

Lin SUN received his M.S. degree from Shandong University in 2011. His research interests include descriptor systems.

Yu ZHENG received his M.S. degree from Shandong University in 2011. His research interests include descriptor systems.

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Yao, J., Feng, Je., Sun, L. et al. Input-output finite-time stability of time-varying linear singular systems. J. Control Theory Appl. 10, 287–291 (2012). https://doi.org/10.1007/s11768-012-1143-2

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  • DOI: https://doi.org/10.1007/s11768-012-1143-2

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