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Analysis Of Oscillations In Nonlinear Systems Using Multiple Input Describing Functions, Frederic Lee Swern

Dissertations

Sufficient conditions for oscillation as well as absence of oscillations are presented for a class of systems containing one lumped linear element and a differentiable nonlinearity. The results are obtained by estimating the error inherent in using a describing function analysis. Contraction type arguments are used to show common topological properties of the describing function solution and the balance of first harmonic terms of the system.

After discussing the describing function method, two theorems are presented regarding existence or nonexistence of oscillations from homotopic considerations. A graphical method for examining systems with power law nonlinearities is given using a parameter …