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Titlebook: Dynamics, Bifurcations and Control; Fritz Colonius,Lars Grüne Conference proceedings 2002 Springer-Verlag Berlin Heidelberg 2002 Analysis.

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A Linearization Principle for Robustness with Respect to Time-Varying Perturbationson linearization theory we show that in discrete time the linearization completely determines the local robustness properties at exponentially stable fixed points of nonlinear systems. In the continuous time case we present a counterexample for the corresponding statement. Sufficient conditions for
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Feedback Equivalence to Feedforward Forms for Nonlinear Single-Input Systemsessary and sufficient conditions to bring the homogeneous terms of any fixed degree of the system into homogeneous feedforward form. If those conditions are satisfied, this leads to a constructive procedure which transforms the system, step by step, into feedforward form. We also formulate a similar
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https://doi.org/10.1007/978-1-4684-8742-8exhibits a rich and complex dynamic when a control parameter is varied. A numerical analysis reveals Hopf, fold and homoclinic bifurcations as the main phenomena. It is shown that the pendulum can be stabilized in its inverted position with zero velocity of the disk if the controller’s gains are appropriately chosen.
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