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For power systems with detailed excitation and power system stabiliser (PSS) controller, the authors set up a singular perturbation dynamical model with saturation non-linearities for their small-signal stability analysis. To estimate the stability region of this kind of dynamical systems, they establish a set of conditions under which the stability region can be decomposed into the Cartesian product of a contractive high-dimensional ellipse and a sufficiently large set. A method is provided for estimating the stability region with least conservativeness by introducing an linear matrix inequality-based optimisation model. A simulation on a simple power system is described as well. Singular perturbation method is a useful tool for the dynamic systems with multi-time scale including the power systems [14-19] and the reference therein. In particular,

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Abstract. Precision Agriculture seeks to match resource application and agronomic practice with soil and crop requirements as they vary in both space and time. Therefore, an understanding of both the temporal and the spatial components of variability is essential before decisions can be made about the feasibility of site‐specific management. In the present study, the spatial and the temporal components of variability in certain key soil properties of a grassland field were evaluated to assess the likely feasibility of adopting a site‐specific approach to grassland management. A 7.9 ha grassland field was selected for the study and soil samples were taken three times at regular 25 m intervals across the field over a two year period, and chemically analysed. Classical and geostatistical procedures were used to evaluate the spatial variability and the temporal stability of soil property distributions. Soil extractable P and K had the greatest within‐field variability and soil pH the least. Soil K distributions were also highly unstable over time and it was concluded that the optimal risk aversion strategy would be to apply uniform dressings of this nutrient to the entire field. In contrast, soil pH, P, Mg and sulphate distributions were not only temporally stable, but were also spatially correlated over reasonably large ranges. It was concluded that these properties might be managed in a site‐specific way based on the results of periodic soil testing in three clearly defined management sub‐units within the field. Over the two year period, C and N accumulated in the soil at surprisingly high rates on certain parts of the field but not in others.

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