Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay

Abstract

Synchronization of cellular neural networks with time-varying delay is discussed in this letter. Based on Razumikhin theorem, a guaranteed cost synchronous controller is given. Unlike Lyapunov-Krasovskii analysis process, there is no constraint on the change rate of time delay. The saturated terms emerging in the Razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by Lipschitz condition and vector inequality, which will bring more conservatism. Then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form, with the help of a sufficient and necessary transformation condition. The minimization of the guaranteed cost is studied, and a further criterion for getting the controller is presented. Finally, the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time-varying delay cellular neural networks.

Robust guaranteed cost control for time‐delay fractional‐order neural networks systems

“…Remark The present method used in Theorem can be regarded as an extension of the problem of guaranteed cost control for integer‐order neural networks systems with time delay (see, eg, the works of He et al) to fractional‐order ones. To the best of our knowledge, this is the first time that the problem of guaranteed cost control of delayed FONNs systems is investigated.…”

“…Remark It should be noted that when α = 1, the quadratic cost function is turned into the definition of cost function in integer‐order systems, which have been considered in the literature …”

“…For neural networks systems, there have been some efforts to tackle the guaranteed cost controller design for neural networks systems in the literature. For example, based on the Razumikhin theorem approach, the problem of guaranteed cost control for cellular neural networks with time‐varying delay was considered in the works of Tu and He and He et al The result of aforementioned works was later improved in the other work of He et al By using Lyapunov‐Krasovskii functional method, the optimal guaranteed cost synchronization problem for a class of coupled neural networks with Markovian jump parameters and mode‐dependent mixed time‐delay was solved in the work of He and Li . Recently, He et al studied the problem of guaranteed cost antiwindup stabilization of discrete delayed cellular neural networks based on the basis of Lyapunov‐Krasovskii theorem and linear matrix inequality formulation.…”

Guaranteed Cost Control for Exponential Synchronization of Cellular Neural Networks with Mixed Time-Varying Delays via Hybrid Feedback Control

“…The guaranteed cost control of uncertain systems was first put forward by Chang and Peng [19] and introduced by a lot of authors, which is to design a controller to robustly stabilize the uncertain system and guarantee an adequate level of performance. The guaranteed cost control approach has recently been extended to the neural networks with time delay (see [7,9,[20][21][22] and references cited therein). In [7], author investigated the guaranteed cost control problem for a class of neural networks with various activation functions and mixed time-varying delays in state and control.…”

“…By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, the sufficient conditions for the existence of an optimal guaranteed cost state feedback for the system have been derived in terms of LMIs. Moreover, all this work has been developed for the guaranteed cost control synchronization of time-varying delay systems [21][22][23][24]. Based on the Lyapunov-Krasovskii analysis process and the zoned discussion and maximax synthesis (ZDMS) method, the quadratic matrix inequality (QMI) criterion for the guaranteed cost synchronous controller is designed to synchronize the given neural networks with time-varying delay [21,22].…”