Quantized ${\mathcal {H}}_\infty$ stabilization for delayed memristive neural networks

Abstract

The issue of ${\mathcal {H}}_{\infty }$ stabilization for delayed memristive neural networks with dynamic quantization is considered. The aim is to design a quantized sampled-data controller guaranteeing that the closed-loop system is globally asymptotically stable with a prescribed ${\mathcal {H}}_{\infty }$ disturbance attenuation level. By means of set-valued maps and the differential inclusion theory, the network under consideration is transformed into a dynamic model subject to time-dependent bounded uncertainty. Then, two different time-dependent two-sided loop functionals are constructed for the non-necessarily and necessarily differential time delay situations, respectively. Two sufficient conditions on the stability and ${\mathcal {H}}_{\infty }$ performance are derived via using these constructed functionals and a few inequality techniques. On the foundation of these conditions, co-designs of the needed feedback gain and dynamic quantization parameter are presented. Finally, three examples are provided to verify the applicability of the quantized sampled-data controller design methods.