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Existence of decoupling normalizing transformations. (English) Zbl 0794.93053
Summary: The existence of normalizing transformations completely decoupling the stable dynamic from the center manifold dynamic is proved.
MSC:
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
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References:
[1] Carr, J., Applications of centre manifold theory, (1981), Springer New York · Zbl 0464.58001
[2] Joshi, M.C.; Bose, R.K., Some topics in nonlinear functional analysis, (1985), Wiley New York · Zbl 0596.47038
[3] Kelly, A., The stable, center-stable, center, center-unstable, unstable manifolds, J. diff. eqns., 3, 546-570, (1967) · Zbl 0173.11001
[4] S. Nikitin, Approximation of decoupling normalizing transformations and local stabilization of nonlinear systems, System Control Lett., submitted. · Zbl 0863.34013
[5] Rouche, N.; Habets, P.; Laloy, M., Stability theory by Lyapunov’s direct method, (1977), Springer New York · Zbl 0364.34022
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