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

Abstract : 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.
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Submitted on : Monday, January 28, 2019 - 2:30:50 PM
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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, Wiley, 2019, 29 (8), pp.2406-2421. ⟨10.1002/rnc.4497⟩. ⟨hal-01996519⟩

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