title: Stability of discrete time recurrent neural networks and nonlinear optimization problems.
abstract: 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.
authors.affiliation: Department of Mathematics, North Dakota State University, Fargo, ND-58102, USA. Electronic address: Jayant.Singh@ndsu.edu.
authors.forename: Jayant
authors.initials: J
authors.lastname: Singh
authors.affiliation: Department of Mathematics, North Dakota State University, Fargo, ND-58102, USA. Electronic address: nikita.barabanov@ndsu.edu.
authors.forename: Nikita
authors.initials: N
authors.lastname: Barabanov
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D009474:Neurons; D017711:Nonlinear Dynamics
keywords: Global Lyapunov stability; Optimization; Recurrent neural networks