Abstract : Fixed-time stability of a class of nonlinear time-varying systems is investigated using the introduced notions of sub-and sup-homogeneity. These concepts allow the systems (even if they do not admit homogeneous approximations) to be analyzed using the homogeneity of their extensions. Then, finite-time and fixed-time stability properties can be recovered. The proposed stability conditions are not based on Lyapunov arguments. In the last section, an example illustrates the obtained results.
Youness Braidiz, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. On fixed-time stability of a class of nonlinear time-varying systems. IFAC World Congress, Jul 2020, Berlin, Germany. ⟨hal-02614533⟩