Extended dissipativity analysis for delayed markovian jump neural networks via delay-function-based Lyapunov functional.

Abstract

The extended dissipativity issue for delayed markovian jump neural networks (MJNNs) with partially unknown transition rates (PUTRs) is investigated. Unlike conventional Lyapunov-Krasovskii functional (LKF), where positive-definite constraint is directly imposed on matrices, a novel delay-function-based one is constructed. The stringent constraint is transferred to the delay-function itself in this LKF, which provides enhanced freedom for result derivation due to its design flexibility and scalability. Moreover, a more general reciprocally convex inequality (RCI) is proposed where the matrices involved are only required to be symmetric or even real, differing from previous ones. Through the combination of these two methodologies, less conservative delay-dependent criteria are derived which ensure the extended dissipativity of the delayed MJNNs with PUTRs. Finally, two numerical examples are provided to demonstrate the superiority of the proposed approach.