Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Stochastic stability of nonlinear discrete-time Markovian jump systems with time-varying delay and partially unknown transition rates

This paper is concerned with stochastic stability of a class of nonlinear discrete-time Markovian jump systems with interval time-varying delay and partially unknown transition probabilities. A new weighted summation inequality is first derived. We then employ the newly derived inequality to establish delay-dependent conditions which guarantee the stochastic stability of the system. These conditions are derived in terms of tractable matrix inequalities which can be computationally solved by various convex optimized algorithms. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Producing a GIS based multiple criteria analysis tool for regional sustainability assessment: the problem of weighting

Decision support tools will be useful in guiding regions to sustainability. These need to be simple but effective at identifying, for regional managers, areas most in need of initiatives to progress sustainability. Multiple criteria analysis (MCA) is often used as a decision support tool for a wide range of applications. This method allows many criteria to be considered at one time. It does this by giving a ranking of possible options based on how closely each option meets the criteria. Thus, it is suited to the assessment of regional sustainability as it can consider a number of indicators simultaneously and demonstrates how sustainability can vary at small scales across the region. Coupling MCA with GIS to produce maps, allows this analysis to become visual giving the manager a picture of sustainability across the region. To do this each indicator is standardised to a common scale so that it can be compared to other indicators. A weighting is then applied to each indicator to calculate weighted summation for each area in the region. This paper argues that this is the critical step in developing a useful decision support tool. A study being conducted in south west Victoria demonstrates that the weights chosen can have a dramatic impact on the results of the sustainability assessment. It is therefore imperative that careful consideration be given to determining indicator weights in a way that is objective and fully considers the impact of that indicator on regional sustainability.

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

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.

Socio-economic inequalities in women`s fruit and vegetable intakes: a multilevel study of individual, social and environmental mediators

Objective: This study employed a multilevel design to test the contribution of individual, social and environmental factors to mediating socio-economic status (SES) inequalities in fruit and vegetable consumption among women. Design: A cross-sectional survey was linked with objective environmental data. Setting: A community sample involving 45 neighbourhoods. Subjects: In total, 1347 women from 45 neighbourhoods provided survey data on their SES (highest education level), nutrition knowledge, health considerations related to food purchasing, and social support for healthy eating. These data were linked with objective environmental data on the density of supermarkets and fruit and vegetable outlets in local neighbourhoods. Results: Multilevel modelling showed that individual and social factors partly mediated, but did not completely explain, SES variations in fruit and vegetable consumption. Store density did not mediate the relationship of SES with fruit or vegetable consumption. Conclusions: Nutrition promotion interventions should focus on enhancing nutrition knowledge and health considerations underlying food purchasing in order to promote healthy eating, particularly among those who are socio-economically disadvantaged. Further investigation is required to identify additional potential mediators of SES–diet relationships, particularly at the environmental level.

Low birth weight in South Asian babies in Britain: time to reduce the inequalities

Babies born in Britain to women of South Asian ethnic origin are lighter on average than the offspring of women of European origin. The causes have been incompletely elucidated but nutritional factors, low socioeconomic status and maternal pre-pregnancy weight have been implicated. This health inequality has received little policy prioritization in Britain. As further research clarifies reasons for this differential, appropriately targeted preventive strategies need to be implemented.

Personal, social and environmental determinants of educational inequalities in walking: a multilevel study

Objective: To investigate the contribution of personal, social and environmental factors to mediating socioeconomic (educational) inequalities in women’s leisure-time walking and walking for transport.
Methods: A community sample of 1282 women provided survey data on walking for leisure and transport; educational level; enjoyment of, and self-efficacy for, walking; physical activity barriers and intentions; social support for physical activity; sporting/recreational club membership; dog ownership; and perceived environmental aesthetics and safety. These data were linked with objective environmental data on the density of public open space and walking tracks in the women’s local neighbourhood, coastal proximity and street connectivity.
Results: Multilevel modelling showed that different personal, social and environmental factors were associated with walking for leisure and walking for transport. Variables from all three domains explained (mediated) educational inequalities in leisure-time walking, including neighbourhood walking tracks; coastal proximity; friends’ social support; dog ownership; self-efficacy, enjoyment and intentions. On the other hand, few of the variables examined explained educational variations in walking for transport, exceptions being neighbourhood, coastal proximity, street connectivity and social support from family.
Conclusions: Public health initiatives aimed at promoting, and reducing educational inequalities in, leisure-time walking should incorporate a focus on environmental strategies, such as advocating for neighbourhood walking tracks, as well as personal and social factors. Further investigation is required to better understand the pathways by which education might influence walking for transport.

lCT and educational (dis) advantage: families, computers and contemporary social and educational inequalities

Because access to new technologies is unequally distributed, there has been considerable debate about the growing gap between the so-called information-rich and information-poor. Such concerns have led to high-profile information technology policy initiatives in many countries. In Australia, in an attempt to 'redress the balance between the information rich and poor' by providing 'equal access to the World Wide Web' (Virtual Communities, 2002), the Australian Council of Trade Unions, Virtual Communities (a computer/software distributor) and Primus (an Internet provider) in late 1999 formed an alliance to offer relatively inexpensive computer and Internet access to union members in order to make 'technology affordable for all Australians' (Virtual Communities, 2002). In this paper, we examine four families, one of which had long-term Information and Communication Technologies (lCT) access, and three of which took advantage of the Virtual Communities offer to get home computer and Internet access for the first time. We examine their engagement with lCT and suggest that previously disadvantaged family members are not particularly advantaged by their access to lCT.

Equity-focused health impact assessment: a tool to assist policy makers in addressing health inequalities.

In Australasia (Australia and New Zealand) the use of health impact assessment (HIA) as a tool for improved policy development is comparatively new. The public health workforce do not routinely assess the potential health and equity impacts of proposed policies or programs. The Australasian Collaboration for Health Equity Impact Assessment was funded to develop a strategic framework for equity-focused HIA (EFHIA) with the intent of strengthening the ways in which equity is addressed in each step of HIA. The collaboration developed a draft framework for EFHIA that mirrored, but modified the commonly accepted steps of HIA; tested the draft framework in six different health service delivery settings; analysed the feedback about application of the draft EFHIA framework and modified it accordingly. The strategic framework shows promise in providing a systematic process for identifying potential differential health impacts and assessing the extent to which these are avoidable and unfair. This paper presents the EFHIA framework and discusses some of the issues that arose in the case study sites undertaking equity-focused HIA.

Socio-demographic inequalities in the diets of mid-aged Australian women

Objectives: This study reports on the distributions of food and nutrient intakes by socio-demographic factors for a large population sample of mid-aged Australian women participating in the Australian Longitudinal Study on Women's Health.
Design: This cross-sectional population-based study used the Cancer Council of Victoria food frequency questionnaires to derive estimates of food and nutrient intakes.
Setting: Nationwide community-based survey.
Subjects: A total of 10561 women aged 50-55 y, at the time of the survey in 2001.
Results: Analysis showed favourable patterns of food intake, with frequent consumption of many foods that are promoted as components of a healthy diet (eg, fresh fruit, leafy green and other vegetables, bread, cereals, milk and meat). Intakes of both foods and nutrients varied significantly across socio-demographic groups, with unmarried women, and women in 'labouring' occupations (eg, cleaner, factory worker, kitchenhand) having poorer nutrient intake.
Conclusions: Although many mid-aged women in this sample had generally healthful diets, women in certain socio-demographic groups (particularly unmarried women and those in labouring occupations) had nutrient intakes of concern. As well as helping to address the dearth of current data on dietary intakes in the Australian population, the results highlight the need for continued targeted public health strategies aimed at improving diet of women from the various socio-economic backgrounds.