Open AccessAdjoint operator‐based isomorphism realisation and control design for non‐linear systems
Author(s) -
Tao Fazhan,
Deng Mingcong
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0927
Subject(s) - control theory (sociology) , bounded function , mathematics , linear system , hilbert space , robust control , factorization , realisation , stability (learning theory) , operator (biology) , control system , computer science , control (management) , algorithm , pure mathematics , mathematical analysis , physics , quantum mechanics , artificial intelligence , machine learning , electrical engineering , engineering , biochemistry , chemistry , repressor , transcription factor , gene
In this study, a realisation to robust right coprime factorisation and robust stability of non‐linear systems with unknown bounded perturbations are investigated based on inner product of Hilbert spaces. In detail, first, a feasible framework based on inner product is proposed to study robust right factorisation of the perturbed non‐linear systems, which provides fundamental for factorising the systems and guaranteeing robust stability. Second, a condition based on adjoint operators of Hilbert spaces is given for the non‐linear systems with unknown bounded perturbations, according to which a compensator is designed and meanwhile eliminates difficulties in obtaining internal signal of the perturbed non‐linear systems. After that, a realisable design scheme on robust stability is given based on the designed controller and the unimordular property. According to the proposed robust design scheme, the non‐linear systems with unknown bounded perturbations can be handled precisely and effectively. Finally, a simulation example is given to confirm the effectiveness of the proposed methods.