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Content Provider | IEEE Xplore Digital Library |
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Author | Tyukin, I.Y. Steur, E. Nijmeijer, H. van Leeuwen, C. |
Copyright Year | 2008 |
Description | Author affiliation: Head of Lab. for Perceptual Dynamics, RIKEN (Inst. for Phys. & Chem. Res.) Brain Sci. Inst., Wako, Japan (van Leeuwen, C.) || Dept. of Math., Univ. of Leicester, Leicester, UK (Tyukin, I.Y.) || Dept. of Mech. Eng., Eindhoven Univ. of Technol., Netherlands (Steur, E.; Nijmeijer, H.) |
Abstract | We consider the problem of small-gain analysis of asymptotic behavior in interconnected nonlinear dynamic systems. Mathematical models of these systems are allowed to be uncertain and time-varying. In contrast to standard small-gain theorems that require global asymptotic stability of each interacting component in the absence of inputs, we consider interconnections of systems that can be critically stable and have infinite input-output L¿ gains. For this class of systems we derive small-gain conditions specifying state boundedness of the interconnection. The estimates of the domain in which the system¿s state remains are also provided. Conditions that follow from the main results of our paper are non-uniform in space. That is they hold generally only for a set of initial conditions in the system¿s state space. We show that under some mild continuity restrictions this set has a non-zero volume, hence such bounded yet potentially globally unstable motions are realizable with a non-zero probability. Proposed results can be used for the design and analysis of intermittent, itinerant and meta-stable dynamics which is the case in the domains of control of chemical kinetics, biological and complex physical systems, and non-linear optimization. |
Starting Page | 5080 |
Ending Page | 5085 |
File Size | 264372 |
Page Count | 6 |
File Format | |
ISBN | 9781424431236 |
ISSN | 01912216 |
DOI | 10.1109/CDC.2008.4739503 |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 2008-12-09 |
Publisher Place | Mexico |
Access Restriction | Subscribed |
Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subject Keyword | Mathematical model Time varying systems Asymptotic stability State estimation State-space methods Biochemical analysis Nonlinear control systems Biological control systems Control systems Chemical analysis |
Content Type | Text |
Resource Type | Article |
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