AimTree species diversity can increase the stability of ecosystem productivity by increasing mean productivity and/or reducing the standard deviation in productivity. However, stand structure, environmental and socio‐economic conditions influence plant diversity and might strongly influence the relationships between diversity and stability in natural forest communities. The relative importance of these factors for community stability remains poorly understood in complex (species‐rich) subtropical forests.LocationSubtropical area of southern China.Time period1999–2014.Major taxa studiedForest trees.MethodsWe conducted bivariate analyses to examine the mechanisms (overyielding and species asynchrony) underlying the effects of diversity on stability. Multiple regression models were then used to determine the relative importance of tree species diversity, stand structure, socio‐economic factors and environmental conditions on stability. Structural equation modelling was used to disentangle how these variables directly and/or indirectly affect forest stability.ResultsTree species richness exerted a positive effect on stability through overyielding and species asynchrony, and this effect was stronger in mountainous forests than in hilly forests. Species richness positively affected the mean productivity, whereas species asynchrony negatively affected the variability in productivity, hence increasing forest stability. Structural diversity also had a positive effect, whereas population density had a negative effect on stability. Precipitation variability and slope mainly had indirect influences on stability through their effects on tree species richness.Main conclusionsOverall, tree species diversity governed stability; however, stand structure, socio‐economic conditions and environmental conditions also played an important role in shaping stability in these forests. Our work highlights the importance of regulating stand structure and socio‐economic factors in forest management and biodiversity conservation, to maintain and enhance their stability to provide ecosystem services in the face of unprecedented anthropogenic activities and global climate change.

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This paper is concerned with the problem of reachable set estimation for discrete‐time singular systems with bounded input disturbances. Based on the Lyapunov method, a new sufficient condition is established in terms of linear matrix inequality (LMI) to guarantee that the reachable set of discrete‐time singular system is bounded by the intersection of ellipsoids. Then the result is extended to the problem for discrete‐time singular systems with time‐varying delay by utilizing the delay‐dependent approach and free weighting matrices. Two numerical examples are provided to demonstrate the effectiveness of the obtained results proposed in this paper.

This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear systems. Based on the piecewise quadratic Lyapunov function (PQLF), the piecewise fuzzy observer-based controllers are designed for T-S fuzzy bilinear systems. It is shown that the stability for discrete T-S fuzzy bilinear system can be established if there exists a PQLF can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities(LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.

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