ZNN for solving online time-varying linear matrix–vector inequality via equality conversion

In this paper, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online time-varying linear matrix–vector inequality (LMVI) via equality conversion. That is, by introducing a time-varying vector (of which each element is great than or equal to zero), such a time-varying linear inequality can be converted to a time-varying matrix–vector equation. Then, the ZNN model is developed and investigated for solving online the time-varying matrix–vector equation (as well as the time-varying LMVI) by employing the ZNN design formula. The resultant ZNN model exploits the time-derivative information of time-varying coefficients. Computer-simulation results further demonstrate the efficacy and superiority of the proposed ZNN model for solving online the time-varying LMVI (and the converted time-varying matrix–vector equation).