This chapter is concerned with the problems of positivity and stability of nonlinear time-delay systems in the area of neural networks. The concept of positivity is first developed and characterized for various models of neural networks with delays including Hopfield neural networks, bidirectional associative memory neural networks and inertial neural networks. It will be shown by utilizing the property of order-preserving of neuron activation functions that for nonnegative connection weights of neurons, state trajectories of the networks initializing from a positive cone called the admissible set of initial conditions are always nonnegative subject to nonnegative inputs. Then, the exponential stability of positive equilibriums of the underlying models is investigated by a systematic approach involving extended comparison techniques via differential and integral inequalities. Unified conditions for the existence and exponential stability of positive equilibriums are derived in the form of linear programming (LP) conditions with M-matrix, which can be effectively solved by various convex algorithms. Numerical examples and simulations are provided to demonstrate the applicability and effectiveness of the derived theoretical results.
Positivity and Stability of Nonlinear Time-Delay Systems in Neural Networks
Studies in Systems, Decision and Control
Recent Advances in Control Problems of Dynamical Systems and Networks ; Chapter : 15 ; 337-385
2020-08-11
49 pages
Article/Chapter (Book)
Electronic Resource
English
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