Research articlePassivity analysis of neural networks with two different Markovian jumping parameters and mixed time delays

- The Markovian jumping parameters in connection weight matrices and discrete time-varying delay are assumed to be different.
- An appropriate Lyapunov-Krasovskii function is constructed which contains more mode-dependent Lyapunov matrices and the domain of constructed triple integrals not only include the lower region of regular triangular prism, but also include the upper region of regular triangular prism.
- The new integral inequalities are used to estimate the derivatives of the constructed LKF which produce sharper bounds than what Jensen's inequality produces.
- Leakage delay is added to the considered model.

This paper studies the problem of passivity analysis for neural networks with two different Markovian jumping parameters and mixed time delays utilizing some integral inequalities. The integral inequalities produce sharper bounds than what the Jensen's inequality produces, consequently, better results are obtained. The Markovian jumping parameters in connection weight matrices and discrete delay are assumed to be different in the system model. By constructing a new appropriate Lyapunov-Krasovskii functional (LKF), some sufficient conditions are established which guarantee the passivity of the proposed model. Numerical examples are given to show the less conservatism and effectiveness of the proposed method.