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H ∞ control for nonlinear affine systems: a chain‐scattering matrix description approach
Author(s) -
Hong JangLee,
Teng ChingCheng
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.556
Subject(s) - affine transformation , lossless compression , nonlinear system , chain (unit) , context (archaeology) , computer science , matrix (chemical analysis) , mathematics , control theory (sociology) , topology (electrical circuits) , algorithm , control (management) , pure mathematics , physics , artificial intelligence , combinatorics , data compression , paleontology , materials science , quantum mechanics , astronomy , composite material , biology
This paper combines an alternative chain‐scattering matrix description with ( J , J ′)‐lossless and a class of conjugate (− J , − J ′)‐lossless systems to design a family of nonlinear H ∞ output feedback controllers. The present systems introduce a new chain‐scattering setting, which not only offers a clearer expression for the solving process of the nonlinear H ∞ control problem but also removes the fictitious signals introduced by the traditional chain‐scattering approach. The intricate nonlinear affine control problem thus can be transformed into a simple lossless network and is easy to deal with in a network‐theory context. The relationship among these ( J , J ′) systems, L 2 ‐gain, and Hamilton–Jacobi equations is also given. Block diagrams are used to illustrate the central theme. Copyright © 2001 John Wiley & Sons, Ltd.