On Conditions of Oscillations and Multi-Homogeneity

Denis Efimov 1, 2 Wilfrid Perruquetti 1, 2, 3
2 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : The notion of homogeneity in the bi-limit from [1] is extended to local homogeneity and then to homogeneity in the multi-limit. The converse Lyapunov/Chetaev theorems on (homogeneous) system instability are obtained. The problem of oscillation detection for nonlinear systems is addressed. The sufficient conditions of oscillation existence for systems homogeneous in the multi-limit are formulated. The proposed approach estimates the number of oscillating modes and the regions of their location. Efficiency of the technique is demonstrated on several examples.
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Denis Efimov, Wilfrid Perruquetti. On Conditions of Oscillations and Multi-Homogeneity. Mathematics of Control, Signals, and Systems, Springer Verlag, 2016, 28. ⟨hal-01223154⟩

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