l2 induced norm analysis of discrete-time LTI systems for nonnegative input signals and its application to stability analysis of recurrent neural networks

[1]  Teruki Kato,et al.  Analysis of Positive Systems Using Copositive Programming , 2020, IEEE Control Systems Letters.

[2]  Takashi Tanaka,et al.  The Bounded Real Lemma for Internally Positive Systems and H-Infinity Structured Static State Feedback , 2011, IEEE Transactions on Automatic Control.

[3]  Murat Arcak,et al.  Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers , 2020, ArXiv.

[4]  Nikita Barabanov,et al.  Stability analysis of discrete-time recurrent neural networks , 2002, IEEE Trans. Neural Networks.

[5]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[6]  S. Bittanti,et al.  Analysis of discrete-time linear periodic systems , 1996 .

[7]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

[8]  Dimitri Peaucelle,et al.  Analysis and Synthesis of Interconnected Positive Systems , 2017, IEEE Transactions on Automatic Control.

[9]  A. Rantzer.  On the Kalman-Yakubovich-Popov lemma , 1996 .

[10]  Mirjam Dür,et al.  Interior points of the completely positive cone. , 2008 .

[11]  Peter J. C. Dickinson.  AN IMPROVED CHARACTERISATION OF THE INTERIOR OF THE COMPLETELY POSITIVE CONE , 2010 .

[12]  Mirjam Dür,et al.  Copositive Programming – a Survey , 2010 .

[13]  Carsten W. Scherer,et al.  LMI Relaxations in Robust Control , 2006, Eur. J. Control.

[14]  Anders Rantzer.  On the Kalman-Yakubovich-Popov Lemma for Positive Systems , 2016, IEEE Trans. Autom. Control..

[15]  Shahrokh Valaee,et al.  Recent Advances in Recurrent Neural Networks , 2017, ArXiv.