@article{1f20abc28f61414a8facada77dfd853a,
title = "Input-to-state stability for discrete-time nonlinear systems",
abstract = "In this work we study the input-to-state stability (ISS) property for discrete-time nonlinear systems. It is shown that most ISS results for continuous time nonlinear systems in the current literature can be extended to the discrete-time case. Several equivalent characterizations of ISS are introduced and two ISS small-gain theorems are proved for nonlinear and interconnected discrete-time systems. ISS stabilizability is discussed and comparisons with the continuous-time case are made. As in the continuous time framework, where the notion ISS found wide applications, we expect that this notion will provide a useful tool in areas related to stability and stabilization for nonlinear discrete time systems as well.",
keywords = "Discrete time systems, Input-to-state stability, Lyapunov functions, Nonlinear small-gain, Nonlinear stability",
author = "Jiang, {Zhong Ping} and Yuan Wang",
note = "Funding Information: Zhong-Ping Jiang received the B.Sc. degree in mathematics from the University of Wuhan, China, in 1988, the M.Sc. degree in statistics from the Universit{\'e} de Paris-sud, Paris, France, in 1989, and the Ph.D. degree in automatic control and mathematics from the Ecole des Mines de Paris, Paris, France, in 1993. From 1993 to 1998, he held visiting researcher positions in several institutions including INRIA (Sophia-Antipolis), France, the Department of Systems Engineering in the Australian National University, Canberra and the Department of Electrical Engineering in the University of Sydney. In 1998, he also visited several US universities. In January 1999, he joined the Polytechnic University at Brooklyn as an Assistant Professor of Electrical Engineering. His main research interests include stabilization, robust/adaptive nonlinear control and decentralized control with applications to nonholonomic mechanical systems. He has authored or coauthored over 80 refereed technical papers in these areas. Currently, Dr. Jiang is an Associate Editor for Systems & Control Letters, and the International Journal of Robust and Nonlinear Control. He is also on the IEEE Conference Editorial Board. Dr. Jiang is the recipient of a prestigious Queen Elizabeth II Fellowship Award (1998) from the Australian Research Council and a CAREER Award (2000) from the U.S. National Science Foundation. Funding Information: The work of the first author was supported partly by a start-up grant from Polytechnic University and partly by NSF Grant INT-9987317. The work of the second author was supported in part by NSF Grant DMS-9457826. The authors would like to thank Dr. E.D. Sontag for many helpful discussions. The authors would also like to thank the anonymous reviewers for their constructive comments and criticism. ",
year = "2001",
month = jun,
doi = "10.1016/S0005-1098(01)00028-0",
language = "English (US)",
volume = "37",
pages = "857--869",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
number = "6",
}