New Delay-Dependent Synchronization Criteria of Complex Dynamical Networks With Time-Varying Coupling Delay Based on Sampled-Data Control via New Integral Inequality

Arthit Hongsri,Thongchai Botmart,Prem Junsawang,Wajaree Weera

doi:10.1109/access.2021.3076361

Arthit Hongsri, Thongchai Botmart + Show 2 more

Open Access

https://doi.org/10.1109/access.2021.3076361

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Abstract

In this work, the issue of synchronization control for complex dynamical networks with time-varying coupling delay based on sampled-data is addressed. First, the sampled-data control is transformed into the bounded sampling period with time-varying delay. As a result, this model is converted to the investigation for synchronization of complex networks with multiple time-varying delays. Second, an appropriate Lyapunov-Krasovkii functional (LKF) is constructed, which composites of double and triple integral terms in quadratic form. Third, we propose a new integral inequality including a reciprocally convex technique which leads to a better condition. Fourth, the solution for the controller gain matrix is obtained by solving linear matrix inequalities (LMIs) with available software such that the synchronization error system is exponentially stable. Finally, the effectiveness and less conservatism of our proposed method are demonstrated via numerical examples.

Highlights

Many types of complex dynamical networks (CDNs) can be described in natural phenomenon for example the social networks, internet, electrical power grids, and food webs [1] etc
To apply with CDNs, in [40], [41], the synchronization of general CDNs with time-varying coupling delay was achieved by designing sampled-data control and Jensen inequality to estimate some of integral term of Lyapunov functional
To derive tighter upper bound on Jensen inequality, [43], [46], [47] achieve synchronization for complex dynamical networks which include time-varying coupling delay based on sampled-data control by using Wirtinger-based integral inequality

Summary

INTRODUCTION

Many types of complex dynamical networks (CDNs) can be described in natural phenomenon for example the social networks, internet, electrical power grids, and food webs [1] etc. To apply with CDNs, in [40], [41], the synchronization of general CDNs with time-varying coupling delay was achieved by designing sampled-data control and Jensen inequality to estimate some of integral term of Lyapunov functional. VOLUME 9, 2021 for sampled-data control of exponential synchronization of complex dynamical networks including time-varying coupling delay was addressed by establishing time-dependent LKF, which includes more detail about sampling term and deals with improved Jensen inequality. To derive tighter upper bound on Jensen inequality, [43], [46], [47] achieve synchronization for complex dynamical networks which include time-varying coupling delay based on sampled-data control by using Wirtinger-based integral inequality. Less conservative criteria of synchronization for complex dynamical networks including time-varying coupling delay based on sampled-data control can be obtained. Our methods can be applied in synchronization of delayed neural networks to get better results with regard to the above schemes

MAIN RESULTS

NUMERICAL EXAMPLES

CONCLUSION