Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach

Abstract

This paper investigates the passivity analysis problem of a class of fractional-order neural networks with interval parameter uncertainties (FONNs-IPUs). The previous IPU processing methods are mainly divided into three categories, i.e., directly using the maximum upper bound matrix or the minimum lower bound matrix, using the combination of these two matrices, and using the maximum norm bound matrix. These methods have some shortcomings, for example, the coupling of information between different intervals and the effect of the negative sign of connection weight are not considered. In order to better analyze the passivity of FONNs-IPUs, firstly, a novel treatment approach of IPUs called interval matrix polytope is proposed, which considers all possible boundary information matrices and the sign of IPUs. Secondly, based on the interval matrix polytope approach, the passivity criteria of FONNs-IPUs are established in linear matrix inequality forms. Finally, the effectiveness of the theoretical results is illustrated by simulation example.