Stability of Solutions to Systems of Nonlinear Differential Equations with Discontinuous Right-Hand Sides: Applications to Hopfield Artificial Neural Networks

In this paper, we study the stability of solutions to systems differential equations with discontinuous right-hand sides. We have investigated nonlinear and linear equations. Stability sufficient conditions for are expressed as a logarithmic norm coefficients Jacobian side system Sufficient in terms norms sides (for equations) following advantages: (1) investigating different metrics from same standpoints, obtained set conditions; (2) easily expressed; (3) robustness areas determined respect variation their parameters; (4) case impulse action, information on moments impact distribution is not required; (5) method obtain extended other definitions (in particular, p-moment stability). The used Hopfield neural networks synapses activation functions.