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

  • Nguyen Thu Ha
  • Nguyen Huu Du
  • Do Duc Thuan
Original Article


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.


Implicit dynamic equations Time scales Convergence Stability domain Spectrum Exponential stability Stability radius 

Mathematics Subject Classification

06B99 34D99 47A10 47A99 65P99 



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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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  1. 1.Department of Basic ScienceElectric Power UniversityHanoiVietnam
  2. 2.Department of Mathematics, Mechanics and InformaticsVietnam National UniversityHanoiVietnam
  3. 3.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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