We consider the nonlinear dynamic system x Δ t a t g y t , y Δ t −f t, x σ t. We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.
The ocurrence of limit cycle phenomena in digital filter structures has been a serious limitation to the use of recursive implementations. The situation is aggravated when fixed point arithmetics is used in the recursive structure. This work introduces a technique to synthesize digital filter structures that are basically "passive", pretending by this procedure a way to avoid the presence of zero-input limit cycles in the final realization. The synthesis process is derived for a general nth order realization. An illustrative case is included.
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