Dissipativity of impulsive matrix-valued neural networks with leakage delay and mixed delays

Abstract

A generalization of real-, complex-, and quaternion-valued neural networks is represented by matrix-valued neural networks (MVNNs), for which the states and weights are matrices. The dissipativity of impulsive MVNNs with leakage delay and mixed delays is studied in this paper, by giving sufficient criteria expressed in terms of real-valued linear matrix inequalities. After decomposing the MVNNs into real-valued systems, Lyapunov–Krasovskii functionals with double, triple, and quadruple integral terms are formulated. Also, the free weighting matrix method, simple, double, and triple Jensen inequalities, the reciprocally convex combination inequality, and the Wirtiger-based integral inequality are used to establish the sufficient criteria. Two numerical examples illustrate the feasibility and correctness of the proposed theoretical results.