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Journal Articles Mathematics of Control, Signals, and Systems Year : 2016

On Conditions of Oscillations and Multi-Homogeneity

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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Dates and versions

hal-01223154 , version 1 (02-11-2015)

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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⟩
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