Stability and robust stability of positive linear Volterra difference equations
作者： Pham Huu Anh Ngoc , Toshiki Naito , Jong Son Shin , Satoru Murakami
DOI: 10.1002/RNC.1335
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摘要: We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability Furthermore, get new Perron–Frobenius theorem Finally, study robust equations under structured perturbations and affine perturbations. Two bounds with respect to these are given. Copyright © 2008 John Wiley & Sons, Ltd.
sci-hub.se 参考文章(41)
Wassim M. Haddad, VijaySekhar Chellaboina, Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay Springer, Berlin, Heidelberg. pp. 421- 435 ,(2004) , 10.1007/978-3-642-18482-6_29
Mark Grigorievich Krein, None, Linear operators leaving invariant a cone in a Banach space Amer. Math. Soc. Transl. Ser. I. ,vol. 10, pp. 199- 325 ,(1950)
Tetsuo FURUMOCHI, Satoru MURAKAMI, Yutaka NAGABUCHI, Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays Japanese journal of mathematics. New series. ,vol. 30, pp. 387- 412 ,(2004) , 10.4099/MATH1924.30.387
V. Rumchev, G. James, Stability of positive linear discrete-time systems Systems science. ,vol. 30, pp. 51- 67 ,(2004)
Stéphane Gaubert, Jeremy Gunawardena, The Perron-Frobenius theorem for homogeneous, monotone functions Transactions of the American Mathematical Society. ,vol. 356, pp. 4931- 4950 ,(2004) , 10.1090/S0002-9947-04-03470-1
Pham Huu Anh Ngoc, Toshiki Naito, Jong Son Shin, On stability of a class of positive linear functional difference equations Mathematics of Control, Signals, and Systems. ,vol. 19, pp. 361- 382 ,(2007) , 10.1007/S00498-007-0018-4
M.R. Crisci, V.B. Kolmanovskii, E. Russo, A. Vecchio, Stability of difference Volterra equations: Direct Liapunov method and numerical procedure Computers & Mathematics With Applications. ,vol. 36, pp. 77- 97 ,(1998) , 10.1016/S0898-1221(98)80011-4
D. J. G. James, S. P. Kostova, V. G. Rumchev, Pole-assignment for a class of positive linear systems International Journal of Systems Science. ,vol. 32, pp. 1377- 1388 ,(2001) , 10.1080/00207720110065531
P.E. Kloeden, A.M. Rubinov, A generalization of the Perron-Frobenius theorem Nonlinear Analysis-theory Methods & Applications. ,vol. 41, pp. 97- 115 ,(2000) , 10.1016/S0362-546X(98)00267-3
Yihong Song, Christopher T.H. Baker†, Perturbation of Volterra Difference Equations Journal of Difference Equations and Applications. ,vol. 10, pp. 379- 397 ,(2004) , 10.1080/10236190310001625253