Non-fragile dissipative state estimation for semi-Markov jump inertial neural networks with reaction-diffusion

Abstract

In this paper, the non-fragile dissipative state estimation is addressed for semi-Markov jump inertial neural networks with reaction-diffusion. A semi-Markov jump model is used to describe the stochastic jump parameters in networks. Different from the invariable transition probabilities in the traditional Markov jump systems, the transition probabilities of the semi-Markov jump systems rely on the stochastic sojourn-time. Accordingly, the Weibull distribution taking the place of the exponential distribution in this paper is adopted for the sojourn-time of each mode in the system. Firstly, by utilizing an applicable vector substitution, the second-order differential system could be converted into the first-order one. Afterwards, via constructing a seemly Lyapunov function of the semi-Markov inertial neural networks and adequately taking advantage of the peculiarities of cumulative distribution functions, some sufficient conditions with less conservatism are constructed to assure that the estimation error system is strictly (R1,R2,R3)−ϱ−dissipative stochastically stable. Based on these conditions, mode-dependent estimator gains are designed. Finally, a numerical example is proposed to validate the availability of the provided approach.