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Xue Yusheng(Nanjing Automation Research Institute,210003,Nanjing,China)  
Numerical integration can show accurate trajectory of the disturbed system,however,no quantitative answer to stability can be given.Lyapunov functions provide sole sufficient but not necessary condition for autonomous systems stability,so that they are not suitable for quantitatively studying motion stability.For non-conservative or nonautonomous systems,it is very difficult to develop Lyapunov functions with meaningful stability domain, and the guarantee on sufficient condition for stability might be lost by using Lyapunov-like functions. The Complementary-Cluster Energy-Barrier Criterion (CCEBC) developed in this paper is a rigorous theory and quantitative method for nonautonomous motion stability. Many relevant problems are studied in the paper. The Extended Equal-Area Criterion (EEAC) for power system transient stability, which has been used in engineering projects, is just such an example.
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