This paper investigates the exponential mixed \(\mathcal {H} _{\infty }/\mathcal {L}_{2}-\mathcal {L}_{\infty }\) state estimation for Markov switching memristive neural networks (MNNs) with time-varying delays. First, in addition to Markov switching parameters, the random variables that obeys Bernoulli distribution are also involved in the MNN model, and thus the considered system model is much more general. Second, the solution in Filippov’s sense is used to transform the Markov switching MNNs into a stochastic system with interval parameters. Third, the reciprocally convex combination technique and an appropriate Lyapunov-Krasovskii functional containing multiple integrals are used to derive less conservative conditions ensuring the existence of the desired state estimators. Finally, a numerical example is provided to show the validity of the proposed method.
