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Robust stability of linear time-varying implicit dynamic equations: a general consideration

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Abstract

In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equations. A formula of stability radius with respect to dynamic structured perturbations acting on the right-hand side coefficients is obtained. In case where structured perturbations affect on both derivative and the right-hand side, the lower bounds for the stability radius are derived. The results are novel and extend many previous results about robust stability for time-varying ordinary differential/difference equations, time-varying differential algebraic equations and time-varying implicit difference equations.

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Acknowledgements

The first and second authors were supported by NAFOSTED project 101.01-2017.302. The third and fourth authors were supported by NAFOSTED project 101.03-2017.308. A part of this work was done when D.D. Thuan was working at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and hospitality. The authors also gratefully thank the reviewers for useful comments that led to the improvements of the paper.

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Correspondence to Do Duc Thuan.

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Thuan, D.D., Nguyen, K.C., Ha, N.T. et al. Robust stability of linear time-varying implicit dynamic equations: a general consideration. Math. Control Signals Syst. 31, 385–413 (2019). https://doi.org/10.1007/s00498-019-0242-8

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  • DOI: https://doi.org/10.1007/s00498-019-0242-8

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