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Stability and robust stability of positive linear Volterra difference equations
Author(s) -
Ngoc Pham Huu Anh,
Naito Toshiki,
Shin Jong Son,
Murakami Satoru
Publication year - 2008
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1335
Subject(s) - mathematics , volterra equations , stability (learning theory) , affine transformation , class (philosophy) , exponential stability , volterra integral equation , mathematical analysis , nonlinear system , integral equation , pure mathematics , computer science , physics , quantum mechanics , machine learning , artificial intelligence
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.