The synchronization of delayed neural networks (DNNs) on time scales is discussed via dynamic output feedback (DOF) method. Two types of DOF controllers are designed: (i) Controller related to the dynamic output state; (ii) Controller both related to the dynamic output state and the output error. Under the action of controllers, the slave system is exponentially synchronized to the master system. A generalized Halanay inequality on time scales is presented. By the Lyapunov functional and the proposed Halanay inequality, some synchronization criteria in LMI form regarding to DNNs on time scales are obtained. A numerical example illustrates the validity of the controllers.

Although optical circuit switch (OCS) based data center network (DCN) can offer high-bandwidth and low-power consumption interconnection for server blocks, it has slow reconfiguration speed and thus is not well-suited to handling highly bursty traffic. Despite several Valiant load-balancing (VLB) type algorithms designed to mitigate this mismatch, they cause notable residual traffic fluctuation, measured by second moment of traffic rate. This leads to a notable tail distribution of flow completion time (FCT). Thereby, this paper proposes a second-moment VLB (sVLB), leveraging the fact that all optical links from the same source rarely burst simultaneously. Different from previous VLB-type algorithms, sVLB utilizes spare capacity in the DCN for load balancing. Specifically, it offloads the bursty traffic from optical links to other intermediate blocks, employing only spare capacity on temporarily idle optical links, and these blocks subsequently route the bursty traffic to its destination. We introduce an sVLB-based framework, which additionally provides a suitable optical topology for sVLB to work with and a weight-based scheme to assist sVLB in intermediate block selection during bursty traffic offloading. Our qualitative assessment and extensive simulation demonstrate that the sVLB-based framework can smooth out the residual traffic fluctuation, thus outperforming existing strategies in normalized FCT.

In this article, asynchronous sliding-mode control (SMC) is investigated for 2-D discrete-time Markov jump systems. As the system modes are not always accessible to the controller, the hidden Markov model is employed to describe the asynchronization between the system modes and controller. A new 2-D sliding surface is constructed and the corresponding asynchronous SMC law is designed under the framework of the hidden Markov model. By Lyapunov function and linear matrix inequality (LMI) approaches, the reachability of system dynamics to the predefined sliding surface is investigated, and sufficient conditions are established to guarantee that the underlying 2-D system is asymptotically mean-square stable (AMSS) with an$H_{\infty }$disturbance attenuation performance. Then, an algorithm is provided to derive the asynchronous 2D-SMC law. Finally, an example is given to verify the validity and effectiveness of the new SMC law design algorithm.