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On finite‐time robust stabilization via nonlinear state feedback
Author(s) -
Zimenko K.,
Polyakov A.,
Efimov D.
Publication year - 2018
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.4292
Subject(s) - lyapunov function , integrator , control theory (sociology) , nonlinear system , constructive , computation , mathematics , control lyapunov function , lyapunov redesign , computer science , control (management) , algorithm , process (computing) , computer network , physics , bandwidth (computing) , quantum mechanics , artificial intelligence , operating system
Summary A nonlinear control law is designed for finite‐time stabilization of a chain of integrators. The method is based on the implicit Lyapunov function technique and homogeneity properties. The scheme of control parameter selection is presented by a linear matrix inequality. The method is simple in implementation and does not assume an online procedure for the computation of the implicit Lyapunov function value at the current state that is an improvement with respect to the works of Polyakov et al. The control law is presented in an explicit form and allows finding the values of all control parameters that make the solution one of the most constructive. The theoretical results are supported by numerical examples.