NDLI: On linearized stability of differential repetitive processes and iterative learning control

Content Provider	IEEE Xplore Digital Library
Author	Altin, Berk Barton, Kira
Copyright Year	2015
Description	Author affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, 48109, USA (Altin, Berk) \|\| Department of Mechanical Engineering, University of Michigan, Ann Arbor, 48109, USA (Barton, Kira)
Abstract	Repetitive processes are two dimensional (2D) systems that arise in the modeling of engineering applications such as additive manufacturing, in which information propagation occurs along two axes of independent variables. While the existing literature on repetitive processes is predominantly on linear systems, recent work highlights the need to develop rigorous tests for stability of nonlinear processes. Using existing results from linear repetitive process theory, we establish a differential repetitive process analogue of the well known result that the stability of a nonlinear feedback system can be verified by the stability of the linearized dynamics. In particular, we employ a 2D Lyapunov equation to show that the feasibility of a linear matrix inequality, combined with 2 small gain conditions, can guarantee stability locally around an equilibrium. Finally, we apply this result to the design and stability analysis of iterative learning control (ILC) systems, and discuss implications in the context of nonlinear ILC.
Starting Page	6064
Ending Page	6069
File Size	321408
Page Count	6
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7403173
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability analysis Asymptotic stability Linear systems Lyapunov methods Laser stability Process control Mathematical model
Content Type	Text
Resource Type	Article

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