Stabilization control of generalized type neural networks with piecewise constant argument (Q2812426)

Generalized neural network described by a set of ordinary scalar semilinear differential equations with deviating arguments and with piecewise constant coefficients is considered. Generalized network means that the state variables in every differential equation can be both delayed and advanced. The semilinear ordinary differential state equation contains both pure linear and pure nonlinear parts. The main purpose of the paper is to formulate and to prove several sufficient conditions for general three types of stabilization, i.e. single state stabilization, multiple state stabilization and output stabilization. In the proofs the theory of delayed ordinary differential equations and the Gronwall-Bellman inequality is used. Moreover, remarks and comments on stabilization problems for neural networks dynamical systems and relationships to the results known on this topic in the literature are also given. Finally, two numerical illustrative examples are also presented. It should be pointed out, that similar problems have been considered in the paper [\textit{X Liao}, \textit{G. Chen} and \textit{E. N. Sanchez}, ``Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach'', Neural Networks 15, No. 7, 859--866 (2002; \url{doi:10.1016/S0893-6080(02)00041-2})].