On Conditions of Oscillations and Multi-Homogeneity

Denis Efimov (1) , Wilfrid Perruquetti (1, 2)

1 NON-A - Non-Asymptotic estimation for online systems
2 Centrale Lille

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.

Mots clés: Oscillations; Index Terms Nonlinear systems; Homogeneity; Instability

Domaines: Automatique / Robotique

Denis Efimov, Wilfrid Perruquetti. On Conditions of Oscillations and Multi-Homogeneity. Mathematics of Control, Signals, and Systems, 2016, 28 (3), ⟨10.1007/s00498-015-0157-y⟩. ⟨hal-01223154⟩