Guaranteed cost synchronization of complex networks with uncertainties and time‐Varying delays

Abstract

This article focuses on the problem of Guaranteed cost synchronization of complex networks with uncertainties and time‐Varying delays. Sufficient conditions for the existence of the optimal guaranteed cost control laws are introduced in the light of linear matrix inequalities via the Lyapunov–Krasovskii stability theory. The time‐varying node delays and time‐varying coupling delays are simultaneously regarded in the complex network. The node uncertainties and coupling uncertainties are simultaneously considered as well. Numerical simulations are provided to account for the effectiveness and robustness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works. © 2015 Wiley Periodicals, Inc. Complexity 21: 381–395, 2016

Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays

“…), the network model (2.7) turns into the complex dynamical network presented by He et al [15]. Hence, our network model (2.1) is more generalized than previous network models, which can be regarded as special cases of the complex dynamical network (2.1).…”

“…This is the first time for investigating the guaranteed cost control for exponential function projective synchronization for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays. There are many works consider the guaranteed cost control of complete synchronization for complex dynamical networks with or without coupling delays [15,17,18,20], where the scaling factor is a constant (α(t) = 1). Hence, our results are superior and have greater applicability.…”

“…In [23], the guaranteed cost synchronization control problem of some general complex dynamical networks with delay was investigated and dynamic feedback controller were designed for the pinning control of parts of the nodes in order for the system to achieve the guaranteed cost synchronization. Moreover, the guaranteed cost synchronization of delayed complex dynamical networks with node uncertainties and coupling uncertainties was presented in [15]. So far, unfortunately, there have still been few papers related to the topic of guaranteed cost synchronization of a CDNs with mixed time-varying delays in the dynamical nodes and in the hybrid uncertainties coupling, including constant coupling, discrete time-varying delay coupling, and distributed time-varying delay coupling, simultaneously.…”

“…Firstly, the definition of exponential function projective synchronization for complex dynamical networks is introduced. Secondly, the considered time-varying delays are different from the time-delay case in [15]. The time-varying delays were mixed between discrete and distributed time-varying delays in the dynamical nodes and in hybrid uncertainties asymmetric coupling, simultaneously.…”

Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

“…Fixed delay is an ideal state of time-varying delay. Therefore, time-varying delay should be considered when studying complex networks [28][29][30][31][32].…”