Abstract
The local controllability behavior near an equilibrium is discussed. If the Jacobian of the linearized system is hyperbolic, uniqueness of local control sets is established.
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F. Colonius and W. Du, Hyperbolic control setsand chain control sets. J. Dynam. Control Systems 7 (2001), 49-59.
F. Colonius and W. Kliemann, Limit behavior andgenericity for non-linear control systems. J. Diff. Equations 109 (1994), 8-41.
F. Colonius and W. Kliemann,Controllability and stabilization of one dimensional control systems near bifurcation points. Systems Control Lett. 24 (1995), 87-95.
F. Colonius and W. Kliemann, The dynamics of control.Birkhäuser (2000).
F. Colonius and M. Spadini,Local uniqueness of control sets for non-linear systems. In: Stability and stabilization of nonlinear systems (D. Aeyels, F. Lamnabhi-Lagarrigue, and A. van der Schaft, eds.). Springer-Verlag (1999), 115-135.
W. Coppel, Dichotomies in stability theory. Lect.Notes Math. 629, Springer-Verlag (1978).
S. Grünvogel, Lyapunov spectrum and control sets near singular points (to appear in J. Differ. Equations).
G. Häckl andK. Schneider, Controllability near Takens–Bogdanov points. J. Dynam. Control Systems 2 (1996), 583-598.
A. Paice andF. R. Wirth, Robustness of nonlinear systems and their domains of attraction. In: Advances in Mathematical Systems Theory. A Volume in Honor of D. Hinrichsen (F. Colonius, U. Helmke, D. Prätzel-Wolters, and F. Wirth, eds.) Birkhäuser (2001), 31-54.
E. D. Sontag, Mathematical control theory. Springer-Verlag(1998).
E. Zeidler, Nonlinear functional analysis. Vol.1. Springer-Verlag (1986).
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Colonius, F., Spadini, M. Uniqueness of Local Control Sets. Journal of Dynamical and Control Systems 9, 513–530 (2003). https://doi.org/10.1023/A:1025692218217
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DOI: https://doi.org/10.1023/A:1025692218217