Robust Finite-time stability of homogeneous systems with respect tomultiplicative disturbances

International audienceLyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples

On fixed-time stability of a class of nonlinear time-varying systems

International audienceFixed-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

On finite-time stability of sub-homogeneous differential inclusions

International audienceSub-homogeneity property is introduced and is related to a differential inclusion (DI). It is shown that a nonlinear ordinary differential equation (ODE), which may not admit a homogeneous approximation, can be transformed into a sub-homogeneous DI (which is a homogeneous extension of the original ODE). Using this homogeneous extension, one can directly recover finite-time stability property for some particular classes of nonlinear systems. In the last section, such a sub homogeneity property is used to design a nonlinear finite-time observer

On robustness of finite-time stability of homogeneous affine nonlinear systems and cascade interconnections

International audienceThis paper investigates robustness of finite-time stability property for a homogeneous nonlinear dynamical system with sufficiently small affine inputs. In addition, robust stability conditions are presented for the systems admitting homogeneous approximations at the origin or at infinity. The effects of additional stable unmodeled dynamics in the input channel on robust stability are investigated. The utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time-varying gains