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- Title
Robustness analysis and training of recurrent neural networks using dissipativity theory.
- Authors
Pauli, Patricia; Berberich, Julian; Allgöwer, Frank
- Abstract
Moreover, the limit superior in (16) exists as HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="italic"> </mi><mn>2</mn></msup><mo mathvariant="normal"> </mo><mi> </mi></math> ht . Besides the S-procedure, the proof exploits stochastic independence of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="italic">x</mi><mi mathvariant="italic">k</mi></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="italic">w</mi><mi mathvariant="italic">k</mi></msub></math> ht and of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="italic">z</mi><mi mathvariant="italic">k</mi></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="italic">w</mi><mi mathvariant="italic">k</mi></msub></math> ht , respectively. The subset HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>l</mi><mn>2</mn><mi mathvariant="italic">n</mi></msubsup><mo stretchy="false"> </mo><msubsup><mi>l</mi><mn>2</mn><mi mathvariant="italic">e</mi><mi mathvariant="italic">n</mi></msubsup></math> ht consists of all square-summable sequences.
- Subjects
RECURRENT neural networks; MATRIX inequalities; ROBUST stability analysis; STABILITY of nonlinear systems; STABILITY of linear systems; LINEAR matrix inequalities
- Publication
Automatisierungstechnik, 2022, Vol 70, Issue 8, p730
- ISSN
0178-2312
- Publication type
Article
- DOI
10.1515/auto-2022-0032