Zhang Neural Network for Online Solution of Time-Varying Linear Matrix Inequality Aided With an Equality Conversion

In this paper, for online solution of time-varying linear matrix inequality (LMI), such an LMI is first converted to a time-varying matrix equation by introducing a time-varying matrix, of which each element is greater than or equal to zero. Then, by employing Zhang ´s neural dynamic method, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online the converted time-varying matrix equation as well as the time-varying LMI. Such a ZNN model showed in an explicit dynamics exploits the time-derivative information of time-varying coefficients. In addition, theoretical analysis and results of the proposed ZNN model are discussed and presented to show its excellent performance on solving the time-varying LMI. Computer simulation results further demonstrate the efficacy of the proposed ZNN model for online solution of the time-varying LMI and the converted time-varying matrix equation.