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Stabilization for a class of complex interlaced systems using asymptotical gain
Author(s) -
Ye Huawen,
Kang Jianling,
Liu Guoping,
Gui Weihua
Publication year - 2010
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.168
Subject(s) - control theory (sociology) , nonlinear system , feed forward , passivity , bounded function , stability (learning theory) , mathematics , high gain antenna , state (computer science) , small gain theorem , automatic gain control , class (philosophy) , computer science , control (management) , engineering , control engineering , bandwidth (computing) , artificial intelligence , algorithm , physics , mathematical analysis , amplifier , computer network , electrical engineering , quantum mechanics , machine learning
This paper addresses the stabilization problem of a class of interlaced systems that are not in a strict‐feedforward form and contain some severe nonlinear terms. Bounded control laws in a fractional form are explicitly constructed. The feature of stability analysis allows the closed‐loop system, when it is proven to have no finite escape time, to employ the asymptotical gain, which is obtained from an input‐to‐state stable (ISS) subsystem, to calculate the severe nonlinear terms, and the related estimate in turn guides the assignment of small controls. Together with the use of the passivity theory and the ISS‐based stability criterion, the proposed method requires no small gain analysis although the asymptotical gain is used, and differs from the state‐dependent saturation scheme since the controls do not include saturation functions. As an application, a new stabilizing control law is presented for the well‐known friction ball‐and‐beam system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society