# Robust dissipativity and passivity analysis for discrete-time stochastic T–S fuzzy Cohen–Grossberg Markovian jump neural networks with mixed time delays

Research paper by S. Ramasamy, G. Nagamani, Quanxin Zhu

Indexed on: 03 Jun '16Published on: 02 Jun '16Published in: Nonlinear Dynamics

#### Abstract

In this paper, we have concerned with the problem of dissipativity and passivity analysis for discrete-time stochastic Takagi–Sugeno (T–S) fuzzy Cohen–Grossberg neural networks with mixed time delays. The dynamical system is transformed into a T–S fuzzy model with uncertain parameters and Markovian jumping parameters. By employing the Lyapunov–Krasovskii functional method and linear matrix inequality (LMI) technique, some new sufficient conditions which are delay dependent in the sense that it depends on not only the discrete delay but also the infinitely distributed delay have been established to ensure the transformed fuzzy neural networks to be $$({\mathcal {Q}},{\mathcal {S}},{\mathcal {R}})-\gamma$$- dissipative and passive. Furthermore, the obtained dissipativity and passivity criteria are established in terms of LMIs, which can be easily checked by using the efficient MATLAB LMI toolbox. Finally, three numerical examples are provided to illustrate the effectiveness and less conservativeness of the obtained results.