On the stability in oscillations in a class of nonlinear feedback systems containing numerator dynamics
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This dissertation is the analysis of the existence, local uniqueness and stability properties of almost sinusoidal oscillations in a class of nonlinear control systems. These systems are modeled by nonlinear ordinary differential equations of the form q(D)x + n(p(D)x) = r(t), where p and q are real polynomials, the degree of p is strictly less than the degree of q, n((.)) is an odd continuous function with some additional piecewise differentiability properties, D = d/dt and r(t) is either identically zero or periodic with a nontrivial period.;The analysis uses the classical single-input sinusoidal describing function, averaging and standard perturbation arguments. If a system parameter is sufficiently small, the existence and local uniqueness of an almost sinusoidal oscillation is guaranteed. Furthermore, the stability of the oscillation is easily checked by a modified Routh-Hurwitz test.;Numerical examples illustrating the results are included.