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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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