State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

Abstract

In this paper, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.

State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays

“…Some recent papers [4,16,17,32] are worth mentioning here. In [4], the state estimation problem has been investigated for continuous-time Markovian jumping neural networks with mode-independent discrete-type time-delays.…”

“…In [32], the state estimation problem has been studied for discrete-time neural networks with Markovian jumping parameters and time-varying discrete time-delays under the assumption that only partial entries in the transition probability matrix are known, but the distributed time-delay has not been taken into account. In [16], the state estimation problem has been addressed for a class of discrete-time Markovian jumping neural networks with mixed mode-dependent time-delays, where the discrete time-delay is time-invariant and the distributed time-delay includes mode-dependent lower bound only. So far, to the best of the authors' knowledge, the state estimation problem has not yet been investigated for discrete-time Markovian jumping neural networks with Markov-mode-dependent lower and upper bounds on the distributed delays.…”

Dissipativity Analysis for Discrete Time-Delay Fuzzy Neural Networks With Markovian Jumps

“…Thus, in real applications, we need to estimate the neuron states through available measurements and then exploit the estimated neuron states to obtain the design requirements. Much work has been investigated for the state estimation of the neural networks, see the references [25,26]. It should noted that state estimation problems were also studied for continuoustime T-S fuzzy neural networks in [27][28][29].…”

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

“…Recently, the state estimation for jumping recurrent neural networks with time-varying delays has been discussed in [34]. Further, in [35], the problem of state estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays has been investigated. To the best of authors knowledge, the state estimation of Markovian jumping recurrent neural networks with interval time-varying delays is very important in both theories and applications and is also a very challenging problem.…”