Design and Analysis of a Novel Integral Design Scheme for Finding Finite-Time Solution of Time-Varying Matrix Inequalities

Abstract

Solving linear inequalities is widely used in various fields, and it plays a more and more crucial role in practical engineering applications. However, the existing recurrent neural network models to solve this problem only achieve global convergence without any noise. To overcome this disadvantage, in this article, we propose a novel integral design scheme for finding the robust solution of time-varying matrix inequalities. The core idea of this model is to add an integral term in the construction of the error function to make the model have error memory, so as to eliminate static difference. Meanwhile, appropriate activation functions (AFs) are used in the integral term noise-tolerance zeroing neural network (ITNTZNN) model, which can make error function accomplish finite-time convergence. The noise tolerance property of the ITNTZNN model is proved by theoretical analysis, and the upper limit of convergence time is obtained. Numerical simulative results ulteriorly verify the finite-time and noise-tolerant properties of the ITNTZNN model.