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State‐feedback H ∞ control of nonlinear singularly perturbed systems
Author(s) -
Fridman E.
Publication year - 2001
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.586
Subject(s) - control theory (sociology) , nonlinear system , controller (irrigation) , state (computer science) , affine transformation , mathematics , full state feedback , order (exchange) , construct (python library) , control (management) , linear system , computer science , mathematical analysis , algorithm , physics , pure mathematics , finance , quantum mechanics , artificial intelligence , agronomy , economics , biology , programming language
We study the H ∞ control problem for an affine singularly perturbed system, which is nonlinear in the state variables. Under suitable assumptions on the linearized problem, we construct ε‐independent composite and linear controllers that solve the local H ∞ control problem for the full‐order system for all small enough ε. These controllers solve also the corresponding problem for the descriptor system. The ‘central’ nonlinear controller can be approximated in the form of expansions in the powers of ε. An illustrative example shows that the higher‐order approximate controller achieves the better performance, while the composite (zero‐order approximate) controller leads to the better performance than the linear one. Copyright © 2001 John Wiley & Sons, Ltd.