Stability and robust stability of positive linear Volterra difference equations |
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| Authors: | Pham Huu Anh Ngoc Toshiki Naito Jong Son Shin Satoru Murakami |
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| Affiliation: | 1. Institute of Mathematics, Ilmenau Technical University, Weimarer Stra?e 25, 98693 Ilmenau, Germany;2. Department of Mathematics, The University of Electro‐Communications, Chofu, Tokyo 182‐8585, Japan;3. Department of Applied Mathematics, Okayama University of Science, Ridaicho, Okayama 700‐0005, Japan |
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| Abstract: | We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd. |
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| Keywords: | linear Volterra difference equation positive system uniform asymptotic stability robust stability |
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