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.

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.

Projected socioeconomic disparities in the prevalence of obesity among Australian adults

Objective: To project prevalence of normal weight, overweight and obesity by educational attainment, assuming a continuation of the observed individual weight change in the 5-year follow-up of the national population survey, the Australian Diabetes, Obesity and Lifestyle study (AusDiab; 2000–2005).

Methods: Age-specific transition probabilities between BMI categories, estimated using logistic regression, were entered into education-level-specific, incidence-based, multi-state life tables. Assuming a continuation of the weight change observed in AusDiab, these life tables estimate the prevalence of normal weight, overweight and obesity for Australian adults with low (secondary), medium (diploma) and high (degree) levels of education between 2005 and 2025.

Results: The prevalence of obesity among individuals with secondary level educational attainment is estimated to increase from 23% in 2000 to 44% in 2025. Among individuals with a degree qualification or higher, it will increase from 14% to 30%. If all current educational inequalities in weight change could be eliminated, the projected difference in the prevalence of obesity by 2025 between the highest and lowest educated categories would only be reduced by half (to a 6 percentage point difference from 14 percentage points).

Conclusion: We predict that almost half of Australian adults with low educational status will be obese by 2025. Current trends in obesity have the potential to drive an increase in the absolute difference in obesity prevalence between educational categories in future years.

Implications: Unless obesity prevention and management strategies focus specifically on narrowing social inequalities in obesity, inequalities in health are likely to widen.