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We consider three types of nonsingular smooth transformations of nonlinear systems with control. These transformations are induced by changes of variables in the state space and in the control space and by changes of the independent variable. We introduce the notions of integrable and nonintegrable changes of the independent variable (time scalings) and of time-varying orbital linearization. For integrable time scalings, we show that, in a nonlinear time-independent system with control, they diminish its order and that control-independent integrable time scalings reduce affine time-independent systems to affine time-independent systems that cannot be linearized by a feedback. We obtain conditions for local orbital linearization and time-varying orbital linearization of affine time-independent systems with a single control.
Differential Equations – Springer Journals
Published: Dec 13, 2014
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