Reachable set bounding for nonlinear perturbed time-delay systems: the smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.

Assessment of delay in age-appropriate vaccination using survival analysis

 Assessment of delay in age-appropriate vaccination provides more information about timeliness of vaccination than up-to-date vaccination coverage. The authors applied survival analysis methods to data from a vaccination coverage survey among children aged 13–59 months conducted in Argentina in 2002. By age 19 months, 43% of children (95% confidence interval (CI): 40, 46) were vaccinated with the fourth dose of diphtheria, tetanus, and pertussis (DTP4). By age 13 months, 55% of children (95% CI: 52, 57) were vaccinated with measles-containing vaccine. By age 7 months, 33% of children (95% CI: 27, 40) were vaccinated with the third dose of hepatitis B. Compared with firstborn children, third children were more likely to be delayed for DTP4 (relative risk (RR) = 1.41, 95% CI: 1.22, 1.62), measles-containing vaccine (RR = 1.54, 95% CI: 1.32, 1.78), and the third dose of hepatitis B (RR = 1.31, 95% CI: 1.03, 1.67). Children whose caregivers had completed secondary school were less likely to be delayed for DTP4 (RR = 0.68, 95% CI: 0.52, 0.90) compared with those whose caregivers had not completed primary school. Survival analysis methods were helpful in measuring vaccine uptake and should be considered in future surveys when assessing delay in age-appropriate vaccination. Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved.

Analysis of backward congestion notification with delay for enhanced Ethernet networks

At present, companies and standards organizations are enhancing Ethernet as the unified switch fabric for all of the TCP/IP traffic, the storage traffic and the high performance computing traffic in data centers. Backward congestion notification (BCN) is the basic mechanism for the end-to-end congestion management enhancement of Ethernet. To fulfill the special requirements of the unified switch fabric, i.e., losslessness and low transmission delay, BCN should hold the buffer occupancy around a target point tightly. Thus, the stability of the control loop and the buffer size are critical to BCN. Currently, the impacts of delay on the performance of BCN are unidentified. When the speed of Ethernet increases to 40 Gbps or 100 Gbps in the near future, the number of on-the-fly packets becomes the same order with the buffer size of switch. Accordingly, the impacts of delay will become significant. In this paper, we analyze BCN, paying special attention on the delay. We model the BCN system with a set of segmented delayed differential equations, and then deduce sufficient condition for the uniformly asymptotic stability of BCN. Subsequently, the bounds of buffer occupancy are estimated, which provides direct guidelines on setting buffer size. Finally, numerical analysis and experiments on the NetFPGA platform verify our theoretical analysis.

New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.

Linear functional state bounding for perturbed time-delay systems and its application

This paper considers time-delay systems with bounded disturbances. We study a new problem of finding an upper bound of an absolute value function of any given linear functional of the state vector starting from the origin of the system. Based on the Lyapunov-Krasovskii method combining with the recent Wirtinger-based integral inequality that has just been proposed by Seuret & Gouaisbaut (2013. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 49, 2860-2866), sufficient conditions for the existence of an upper bound of the function are derived. The obtained results are shown to be more effective than those adapted from the existing works on reachable set bounding. Furthermore, the obtained results are applied to refine existing ellipsoidal bounds of the reachable sets. The effectiveness of the obtained results is illustrated by two numerical examples.

On backwards and forwards reachable sets bounding for perturbed time-delay systems

Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov-Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.

A practical functional observer scheme for interconnected time-delay systems

This paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non-instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems. A set of easily verifiable existence conditions is established and upon its satisfaction, simple distributed observers are designed using a straightforward design procedure. Simulation results of a numerical example are given to substantiate the feasibility of the approach.

An enhanced stability criterion for time-delay systems via a new bounding technique

In the past few years, a great deal of effort has been devoted to improve delay-dependent conditions for stability of linear systems with an interval time-varying delay. To reduce conservatism of stability conditions, in the framework of the Lyapunov-Krasovskii functional (LKF) method, the bounding technique plays a key role. In this paper, a new bounding technique based on a new integral inequality is proposed. By employing the newly bounding technique proposed in this paper, an enhanced stability criterion for a class of linear systems with an interval time-varying delay is derived. The effectiveness and a significant improvement of the obtained results are shown by numerical examples.

Design of state observers for interconnected time-delay systems via a coordinate transformation approach

This paper considers the design of state observers for interconnected time-delay systems using a coordinate transformation method. Through such a transformation, the system that has interconnection and state delays is metamorphosed into a new system that injects time-delay information into its input and output terms, before reintroducing them back into the latter system, effectively coupling the delay terms into the IO injection terms and eliminating the delay values from the state variables. Next, full-order and reduced-order observers are designed based on the transformed system. Finally, the observed states of the transformed system that correspond to the original system is used to deduce the estimates of the original system. A numerical example is provided of an interconnected time-delay system.

A fault detection scheme for time-delay systems using minimum-order functional observers

This paper presents a method for designing residual generators using minimum-order functional observers to detect actuator and component faults in time-delay systems. Existence conditions of the residual generators and functional observers are first derived, and then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing minimum-order functional observers to detect faults in the system. The advantages of having minimum-order observers are obvious from the economical and practical points of view as cost saving and simplicity can be achieved, particularly when dealing with high-order complex systems. Extensive numerical examples are given to illustrate the proposed fault detection scheme. In all the numerical examples, we design minimum-order residual generators and functional observers to detect faults in the system.

Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

Abstract
This paper presents new discrete inequalities for single summation and double summation. These inequalities are based on multiple auxiliary functions and include the Jensen discrete inequality and the discrete Wirtinger-based inequality as special cases. An application of these discrete inequalities to analyse stability of linear discrete systems with an interval time-varying delay is studied and a less conservative stability condition is obtained. Three numerical examples are given to show the effectiveness of the obtained stability condition.