A New Free-matrix Inequality with application to Exponential State Estimation for Markov Jump Neural Networks

This paper is concerned with an exponential state estimation problem for a class of Markov Jump Neural Networks (MJNNs) with Time-varying Delay (TVD). Firstly, to derive a tighter bound of Exponential-type Integral Quadratic Terms (EIQTs), a new Free-matrix Exponential-type Inequality (FMEI) is provided, which includes some existing ones as its special cases. Secondly, by fully considering the information of attenuation exponent and TVD, a novel Lyapunov-Krasovskii Functional (LKF) is constructed. Then, by employing the new FMEI and other analytical techniques, a less conservative criterion guaranteeing the stochastic stability of the error system is obtained in form of Linear Matrix Inequalities (LMIs). In the end, a numerical example is given to show the effectiveness of the obtained result.