Nonlinear Dynamics

, Volume 62, Issue 3, pp 543–552

2–ℒ nonlinear system identification via recurrent neural networks

Original Paper

DOI: 10.1007/s11071-010-9741-3

Cite this article as:
Ahn, C.K. Nonlinear Dyn (2010) 62: 543. doi:10.1007/s11071-010-9741-3


This paper proposes an ℒ2–ℒ identification scheme as a new robust identification method for nonlinear systems via recurrent neural networks. Based on linear matrix inequality (LMI) formulation, for the first time, the ℒ2–ℒ learning algorithm is presented to reduce the effect of disturbance to an ℒ2–ℒ induced norm constraint. New stability results, such as boundedness, input-to-state stability (ISS), and convergence, are established in some senses. It is shown that the design of the ℒ2–ℒ identification method can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed identification scheme.


2–ℒ identificationRecurrent neural networksInput-to-state stability (ISS)Linear matrix inequality (LMI)Weight learning law

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Division of Electronics and Control EngineeringWonkwang UniversityIksanKorea