# Further Results on Dissipativity Criterion for Markovian Jump Discrete-Time Neural Networks with Two Delay Components Via Discrete Wirtinger Inequality Approach

Research paper by S. Ramasamy, G. Nagamani; T. Radhika

Indexed on: 18 Oct '16Published on: 30 Sep '16Published in: Neural Processing Letters

#### Abstract

Abstract This paper is concerned with strict $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma$$ - dissipativity and passivity analysis for discrete-time Markovian jump neural networks involving both leakage and discrete delays expressed in terms of two additive time-varying delay components. The discretized Wirtinger inequality is utilized to bound the forward difference of finite-sum term in the Lyapunov functional. By constructing a suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee the dissipativity and passivity criteria of the proposed neural networks. These conditions are presented in terms of linear matrix inequalities (LMIs), which can be efficiently solved via LMI MATLAB Toolbox. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.AbstractThis paper is concerned with strict $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma$$ - dissipativity and passivity analysis for discrete-time Markovian jump neural networks involving both leakage and discrete delays expressed in terms of two additive time-varying delay components. The discretized Wirtinger inequality is utilized to bound the forward difference of finite-sum term in the Lyapunov functional. By constructing a suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee the dissipativity and passivity criteria of the proposed neural networks. These conditions are presented in terms of linear matrix inequalities (LMIs), which can be efficiently solved via LMI MATLAB Toolbox. Finally, numerical examples are given to illustrate the effectiveness of the proposed results. $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma$$ $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma$$