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Bohl–Perron Type Stability Theorems for Linear Singular Difference Equations

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Abstract

In this paper, we investigate certain input-state relations and the exponential stability for singular systems of linear difference equations. For the treatment of singular systems, we use the projector-based approach. Based on the result of decoupling, we construct admissible spaces for the inhomogeneity part of the singular systems. Three so-called Bohl–Perron type stability theorems, which are known in the literature for regular explicit difference equations, are extended to singular difference equations.

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Acknowledgments

This research was partially supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) Project 101.02-2014.05. The research of the second author was also supported by the Thang Long University, Project DTCS047.

The authors thank Prof. Pham Ky Anh and Prof. Nguyen Huu Du for valuable discussions during the preparation of the manuscript. They also thank the anonymous referees for useful comments that led to the improvement of the paper.

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Authors and Affiliations

  1. Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, Hanoi, Vietnam

    Vu Hoang Linh

  2. Faculty of Mathematics and Informatics, Thang Long University, Hanoi, Vietnam

    Ngo Thi Thanh Nga

Authors
  1. Vu Hoang Linh
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  2. Ngo Thi Thanh Nga
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Correspondence to Vu Hoang Linh.

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Linh, V.H., Nga, N.T.T. Bohl–Perron Type Stability Theorems for Linear Singular Difference Equations. Vietnam J. Math. 46, 437–451 (2018). https://doi.org/10.1007/s10013-017-0245-z

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  • DOI: https://doi.org/10.1007/s10013-017-0245-z

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