Finite-time state estimation for jumping recurrent neural networks with deficient transition probabilities and linear fractional uncertainties

This paper is concerned with the finite-time stability and the finite-time boundedness issues on the estimation problem for a class of continuous-time uncertain recurrent neural networks with Markovian jumping parameters. The uncertain parameters are described by the linear fractional uncertainties and the jumping parameters obey the homogeneous Markov process with possibly deficient probability transition matrix. A full-order state estimator is constructed to estimate the neuron state, in presence of the uncertain and jumping parameters, such that the resulting error dynamics of the state estimation is (i) finite-time stable in the disturbance-free case; and (ii) finite-time bounded in case of exogenous disturbances on the measurements. By employing the Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are established that ensure the existence of the desired finite-time state estimator, and then the explicit expression of such state estimators is characterized in terms of the feasibility to a convex optimization problem that can be easily solved by using the semi-definite programme method. Validity and effectiveness of the developed design method are demonstrated by a numerical example.