On homogeneity of discrete-time systems: stability and convergence rates

A new definition of homogeneity for discrete-time systems is introduced. As in the continuous-time case, the property can be verified algebraically in the transition map of the system, and it implies that a dilation of the initial conditions leads to a scaling of the trajectory. Stability properties and convergence rates of the system's solutions can be established by considering only the homogeneity degree. The existence of homogeneous Lyapunov and Lyapunov-like functions is proven.

Mots clés

Homogeneous systems Lyapunov methods Nonlinear systems Discrete-time systems

Domaines

Automatique / Robotique

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Denis Efimov : Connectez-vous pour contacter le contributeur

https://inria.hal.science/hal-01996519

Soumis le : lundi 28 janvier 2019-14:30:50

Dernière modification le : mercredi 24 janvier 2024-09:54:23

Dates et versions

hal-01996519 , version 1 (28-01-2019)

Identifiants

HAL Id : hal-01996519 , version 1
DOI : 10.1002/rnc.4497

Citer

Tonametl Sanchez, Denis Efimov, Andrey Polyakov, Jaime Moreno, Wilfrid Perruquetti. On homogeneity of discrete-time systems: stability and convergence rates. International Journal of Robust and Nonlinear Control, 2019, 29 (8), pp.2406-2421. ⟨10.1002/rnc.4497⟩. ⟨hal-01996519⟩

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