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Date of Award
2016
Publisher
North Dakota State University
Document Type
Dissertation
Degree Awarded
Doctor of Philosophy (PhD)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Barabanov, Nikita
Description
We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems produce rather weak results. The method mentioned above is proved to be more powerful. It involves a multi-step procedure with maximization of special nonconvex functions over polytopes on every step. We derive conditions which guarantee an existence of at most one point of local maximum for such functions over every hyperplane. This nontrivial result is valid for wide range of neuron transfer functions.
Recommended Citation
Singh, Jayant, "Optimization Problems Arising in Stability Analysis of Discrete Time Recurrent Neural Networks" (2016). Mathematics. 20.
https://digitalcommons.ndsu.edu/mathematics/20
Rights
NDSU Policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/25537