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Section: New Results

Robustness of homogeneous systems

Participants : Andrey Polyakov, Denis Efimov.

In [32], we studied the finite-time stability of a class of nonlinear systems $\dot{x}=f\left(x\right)=H\left(x\right)b\left(x\right)$, where $H$ is homogeneous and $b$ is bounded. We defined the homogeneous extension of the non-homogeneous function $f$ and used this extension to prove that, under some conditions on $b$, if the system $\dot{x}=f\left(x\right)$ is globally asymptotically stable, then it is finite-time stable. In [31], a theoretical basement of the previous result has been given showing robust stability of the system $\dot{x}=f\left(x\right)=H\left(x\right)b\left(x\right)$ by considering $b$ as a perturbation.