We design a full-order observer for discrete-time linear time-invariant systems with constant output delays. The observer design is based on the output delay model expressed by a two-dimensional state variable, with discrete-time and space independent variables. Employing a discrete-time state transformation, we construct an explicit strict Lyapunov function that enables us to prove the global exponential stability of the full-order observer error system with an explicit estimate of the exponential decay rate. The numerical example demonstrates the design of the full-order observer and illustrates the validity of the exponential stability.

We improve the cycle time performance of EtherCAT networks with embedded Linux-based master by developing a Linux Ethernet driver optimized for EtherCAT operation. The Ethernet driver is developed to establish a direct interface between the master module and Ethernet controllers of embedded systems by removing the involvement of Linux network stack and the New API (NAPI) of standard Ethernet drivers. Consequently, it is achieved that the time-consuming memory copy operations are reduced and the process of EtherCAT frames is accelerated. In order to demonstrate the effect of the developed Ethernet driver, we set up EtherCAT networks composed of an embedded Linux-based master and commercial off-the-shelf slaves, and the experimental results confirm that the cycle time performance is significantly improved.

We address the stability property of the FAST TCP congestion control algorithm. Based on a continuous-time dynamic model of the FAST TCP network, we establish that FAST TCP in itself is globally exponentially stable without any specific conditions on the congestion control parameter or the update gain. Simulation results demonstrate the validity of the global exponential stability of FAST TCP.

We propose a system time synchronization method between ARM-based embedded Linux systems. The master Linux with reference clock sends its own system time to the slave Linux via Transmission Control Protocol communication along with a general-purpose input/output (GPIO) signal, and then the slave Linux corrects its own system time by the difference between its own system time at receiving the GPIO signal and the received reference time. The synchronization performance is significantly improved by compensating for the GPIO signal detection latency and the system time acquisition and setting latencies in Linux. These latencies are precisely measured by exploiting the function of Cycle Counter register in ARM coprocessor. Extensive experiments are performed with two ARM-based embedded Linux systems, and the results demonstrate the validity and performance of the proposed synchronization method.

We consider a single-link multi-source network with FAST TCP sources. We adopt a continuous-time dynamic model for FAST TCP sources, and propose a static model to adequately describe the queuing delay dynamics at the link. The proposed model turns out to have a structure that reveals the time-varying network feedback delay, which allows us to analyze FAST TCP with due consideration of the time-varying network feedback delay. Based on the proposed model, we establish sufficient conditions for the boundedness of congestion window of each source and for the global asymptotic stability. The asymptotic stability condition shows that the stability property of each source is affected by all other sources sharing the link. Simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

We address the global asymptotic stability of FAST TCP, especially considering cross traffics, time-varying network feedback delay, and queuing delay dynamics at link. Exploiting the inherent dynamic property of FAST TCP, we construct two sequences that represent the lower and upper bound variations of the congestion window in time. By showing that the sequences converge to the equilibrium point of the congestion window, we establish that FAST TCP in itself is globally asymptotically stable without any specific conditions on the tuning parameter α or the update gain γ.

We consider a class of nonlinear time delay systems with time-varying delays, and achieve a time delay independent sufficient condition for the global asymptotic stability. The sufficient condition is proved by constructing a continued fraction that represents the lower and upper bound variations of the system trajectory along the current of time, and showing that the continued fraction converges to the equilibrium point of the system. The simulation results show the validity of the sufficient condition, and illustrate that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for the global asymptotic stability.