NDLI: Norm vanishment and its applications in constrained control

Content Provider	IEEE Xplore Digital Library
Author	Bin Zhou Zongli Lin Guang-Ren Duan
Copyright Year	2009
Description	Author affiliation: Center for Control Theory and Guidance Technology, Harbin Institute of Technology, 150001, China (Bin Zhou; Guang-Ren Duan) \|\| Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, 22904-4743, U.S.A. (Zongli Lin)
Abstract	In Part I of this paper, we introduced the notion of ℒ∞-vanishment and established several kinds of characterizations of this notion. Based on this notion, ℒ∞ low gain feedback was reconsidered and a systematic approach to ℒ∞ low gain feedback design was proposed. In this second part of the paper, we consider the parallel notion of ℒ2-vanishment. We establish several characterizations of the ℒ2-vanishment property, based on which a new design approach referred to as the ℒ2 low gain feedback approach is developed. Just as the ℒ∞ low gain design is useful in the control of linear systems subject to actuator magnitude saturation, the ℒ2 low gain feedback is instrumental in the control of systems with control energy constraints. As applications of ℒ2 low gain feedback, the problem of semi-global stabilization of linear systems with energy constraints and the problem of linear time-delay system with energy constraints are solved in this paper. The notion of ℒ2-vanishment and the resulting ℒ2 low gain feedback are also extended to nonlinear systems. As in the ℒ∞ low gain feedback considered in Part I, a systematic approach is also developed for ℒ2 low gain feedback design in this second part of the paper. Finally, an example involving a linearized model of the relative motion with respect to another in a circular orbit around the Earth is used to illustrate the effectiveness of the results developed in this paper.
Starting Page	7984
Ending Page	7989
File Size	793484
Page Count	6
File Format	PDF
ISBN	9781424438716
ISSN	01912216
DOI	10.1109/CDC.2009.5400858
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-15
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Control systems Linear feedback control systems Linear systems Hydraulic actuators Instruments Nonlinear systems Earth Equations Eigenvalues and eigenfunctions H infinity control
Content Type	Text
Resource Type	Article

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