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On data dependence of stability domains, exponential stability and stability radii for implicit linear dynamic equations

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Abstract

We shall deal with some problems concerning the stability domains, the spectrum of matrix pairs, the exponential stability and its robustness measure for linear implicit dynamic equations of arbitrary index. First, some characterizations of the stability domains corresponding to a convergent sequence of time scales are derived. Then, we investigate how the spectrum of matrix pairs, the exponential stability and the stability radii for implicit dynamic equations depend on the equation data when the structured perturbations act on both the coefficient of derivative and the right-hand side.

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Acknowledgments

The second author was supported financially by Vietnam National Foundation for Science and Technology Development (NAFOSTED) 101.03-2014.58. The third author was supported financially by the Foundation for Science and Technology Development of Vietnam’s Ministry of Education and Training B2016-BKA-03. This work was done while the third author was visiting at Vietnam Institute for Advance Study in Mathematics (VIASM). The third author would like to thank VIASM for support and providing a fruitful research environment and hospitality.

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Authors and Affiliations

  1. Department of Basic Science, Electric Power University, 235 Hoang Quoc Viet Str., Hanoi, Vietnam

    Nguyen Thu Ha

  2. Department of Mathematics, Mechanics and Informatics, Vietnam National University, 334 Nguyen Trai Str., Hanoi, Vietnam

    Nguyen Huu Du

  3. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet Str., Hanoi, Vietnam

    Do Duc Thuan

Authors
  1. Nguyen Thu Ha
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  2. Nguyen Huu Du
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  3. Do Duc Thuan
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Correspondence to Do Duc Thuan.

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Ha, N.T., Du, N.H. & Thuan, D.D. On data dependence of stability domains, exponential stability and stability radii for implicit linear dynamic equations. Math. Control Signals Syst. 28, 13 (2016). https://doi.org/10.1007/s00498-016-0164-7

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  • DOI: https://doi.org/10.1007/s00498-016-0164-7

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