Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

  • Shankar A. DekaEmail author
  • Dušan M. Stipanović
  • Boris Murmann
  • Claire J. Tomlin
Technical Note


In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.


Neural networks Global asymptotic stability Stabilization 

Mathematics Subject Classification

93D20 68T99 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Coordinated Science Laboratory, and MechSE DepartmentUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Electrical Engineering DepartmentStanford UniversityStanfordUSA
  3. 3.EECS DepartmentUniversity of CaliforniaBerkeleyUSA

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