Extended Dissipativity Performance for the Delayed Discrete-Time Neural Networks with Observer-Based Control

This paper is concerned with the problem of extended dissipativity performance for a class of delayed discrete-time neural networks (DNNs) subject to state-feedback observer-based control design. To achieve this, a new improved summation based inequality is proposed by combining the Jensen-based summation inequality and an extended reciprocal convex matrix inequality so as to linearize the summable quadratic terms occurring in the forward difference of the constructed Lyapunov-Krasovskii functional (LKF). The desired results ensuring the extended dissipativity performance for the observer-based error system have been established in terms of linear matrix inequalities (LMIs) by utilizing the developed summation based inequality. Further, the designed state-feedback and observer control gain matrices can be determined by solving the proposed LMIs. Finally, in order to analyze the applicability and effectiveness of the proposed theoretical results, numerical examples including a quadruple tank process (QTP) system model have been illustrated with simulation results.