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Stabilization of state‐constrained switched nonlinear systems in p ‐normal form
Author(s) -
Su Qingyu,
Long Lijun,
Zhao Jun
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2949
Subject(s) - backstepping , control theory (sociology) , bounded function , lyapunov function , nonlinear system , mathematics , state (computer science) , constraint (computer aided design) , control lyapunov function , domain (mathematical analysis) , class (philosophy) , strict feedback form , function (biology) , lyapunov redesign , control (management) , computer science , adaptive control , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , algorithm , evolutionary biology , biology
SUMMARY This paper is concerned with the stabilization problem for a class of state‐constrained switched nonlinear system in p ‐normal form in a domain. A key point in the backstepping design procedure is to find a common stabilizing function at each step. A barrier Lyapunov function, which grows to infinity when its arguments approach some limits, is introduced to ensure that the state constraint is not violated at any time. Bounded state feedback controllers of individual subsystems and a common Lyapunov function are explicitly constructed to asymptotically stabilize the closed‐loop system under arbitrary switchings. An example is given to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.