Floquet theorem for linear implicit nonautonomous difference systems |
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| Authors: | Pham Ky Anh Ha Thi Ngoc Yen |
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| Affiliation: | Department of Mathematics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam |
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| Abstract: | The aim of this paper is to develop the Floquet theory for linear implicit difference systems (LIDS). It is proved that any index-1 LIDS can be transformed into its Kronecker normal form. Then the Floquet theorem on the representation of the fundamental matrix of index-1 periodic LIDS has been established. As an immediate consequence, the Lyapunov reduction theorem is proved. Some applications of the obtained results are discussed. |
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| Keywords: | Implicit difference equations Differential algebraic equations Floquet theorem Lyapunov reduction theorem |
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