On stability and Bohl exponent of linear singular systems of difference equations with variable coefficients |
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Authors: | N H Du N T T Nga |
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Institution: | 1. Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, Hanoi, Vietnam.;2. Faculty of Mathematics and Informatics, Thang Long University, Hanoi, Vietnam. |
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Abstract: | In this paper we investigate the stability of linear singular systems of difference equations with variable coefficients by the projector-based approach. We study the preservation of uniform/exponential stability when the system coefficients are subject to allowable perturbations. A Bohl–Perron type theorem is obtained which provides a necessary and sufficient condition for the boundedness of solutions of nonhomogenous systems. The notion of Bohl exponent is introduced and we characterize the relation between the exponential stability and the Bohl exponent. Finally, robustness of the Bohl exponent with respect to allowable perturbations is investigated. |
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Keywords: | Singular difference equation tractability index canonical projector Cauchy operator exponential stability Bohl exponent |
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