Stability Boundary Characterization of Nonlinear Autonomous Dynamical Systems in the Presence of Saddle-Node Equilibrium Points
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R. Genesio, M. Tartaglia, and A. Vicino, On the estimation of asymptotic stability regions: State of the art and new proposals, Institute of Electrical and Electronics Engineers Transactions on Automatic Contral, 8 (1985), 747-755.
H.D. Chiang, J.S. Thorp., Stability regions of nonlinear dynamical systems: a constructive methodology, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 34, No. 12 (1989), 1229-1241.
F.M. Amaral, L.F.C. Alberto, Stability Boundary Characterization of Nonlinear Autonomous Dynamical Systems in the Presence of a Type-Zero Saddle-Node
Equilibrium Point, Tendências em Matemática Aplicada e Computacional, 11 (2010), 111–120.
F.M. Amaral, L.F.C. Alberto, Stability Region Bifurcations of Nonlinear Autonomous Dynamical Systems: Type-Zero Saddle-Node Bifurcations, International Journal of Robust and Nonlinear Control, 21, No. 6 (2011), 591-612.
L.F.C. Alberto, H.D. Chiang, Uniform Approach for Stability Analysis of Fast Subsystem of Two-Time Scale Nonlinear Systems, Int J Bifurcat Chaos Appl Sci Eng, 17 (2007), 4195-4203.
H.D. Chiang, M.W. Hirsch, F.F. Wu, Stability region of nonlinear autonomous dynamical systems, Institute of Electrical and Electronics Engineers Trans. on Automatic Control, 33, No. 1 (1988), 16-27.
H.D. Chiang, F.Wu, P.P. Varaiya, Foundations of the potential energy boundary surface method for power transient stability analysis, Institute of Electrical and Electronics Engineers Trans. on Circuits and Systems, 35, No. 6 (1988), 712-728.
H.D. Chiang, F. Wu, P.P. Varaiya, Foundations of direct methods for power system transient stability analysis, Institute of Electrical and Electronics Engineers Trans. on Circuits and Systems, 34, No. 2 (1987), 160-173.
H.D. Chiang, L. Fekih-Ahmed, Quasi-stability regions of nonlinear dynamical systems: optimal estimations, Institute of Electrical and Electronics Engineers Trans. on Circuits and Systems, 43 , No. 8 (1996), 636-643.
H.D. Chiang, “Direct Methods For Stability Analysis of Electric Power Systems - Theoretical Foundation" , Bcu Methodologies, And Applications, John Wiley and Sons, 2010.
J. Guckenheimer, P. Holmes, “Nonlinear Oscilations,Dynamical Systems and Bifurcations of Vector Fields”, Springer -Verlag, New York, 1983.
V. Guillemin, A. Pollack, “Differential Topology”, Englewood Cliffs, NJ: Prentice-Hall, 1974.
M.W. Hirsch, C.C. Pugh, M. Shub, Invariant manifolds, Bull. Amer. Math. Soc., 76, No. 5 (1970), 1015-1019.
W. Hurewicz., H. Wallman, “Dimension Theory”, Princeton, NJ: Princeton University Press, 1948.
P. Kokotovic, R. Marino, On vanishing stability regions in nonlinear systems with high-gain feedback, Institute of Electrical and Electronics Engineers Trans. Automat. Contr., 31, No. 10 (1986), 967-970.
R.M. May, “Stability and Complexity in Model Ecosystems”, Princeton, NJ: Princeton University Press, 1973.
M. Loccufier, E. Noldus, A new trajectory reversing method for estimating stability regions of autonomous dynamic systems, Institute of Electrical and Electronics Engineers Nonlinear Dyn., 21 (2000), 265-288.
J. Palis, On Morse-Smale Dynamical Systems, Topology, 8, 385-405.
R.M. Peterman, A Simple Mechanism that Causes Collapsing Stability Regions in Exploited Salmonid Populations, J. Fish. Res. Board Can., 34, 1977.
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967) 747-817.
J. Sotomayor, Generic bifurcations of dynamical systems. In Dynamical Systems, (1973), 549-560.
S. Wiggins, “Introduction to Applied Nonlinear Dynamical Systems and Chaos”, Springer -Verlag, New York, 2003.
DOI: https://doi.org/10.5540/tema.2012.013.02.0143
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