Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach

Abstract

This letter deals with the guaranteed cost stabilization of time-varying delay cellular neural networks (DCNNs). Based on the Razumikhin theorem and via applying the zoned discussion and maximax synthesis method in DCNNs, the quadratic Riccati matrix inequality criterion for the guaranteed cost stabilization controller is designed to stabilize the given chaotic DCNNs. The minimization of the guaranteed cost of stabilization for the DCNNs is also given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost stabilization control and its corresponding minimization problem.

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 Stabilization of Cellular Neural Networks with Time‐Varying Delay

“…By substituting P1 = P -1 , N1 = P1K T into (9), we have (7). It is also easy to prove the necessity by using Lemma 1.…”

“…X12, X22, H, D are real constant matrices of appropriate dimensions. There exist a positive definite matrix P1 and a matrix N1 ∈ R n¥n , and the matrices satisfy the matrix inequality(7) …”