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References in periodicals archive ?
By Invariance Lemma 5 with a linear equivalence [chi](z) = [alpha]z + [beta] ([alpha] = 0) we can assume that [C.sub.i] is the imaginary axis and that [D.sub.i] = G, the open right half-plane, as above.
On the other hand, for the [PDD.sup.1/2] there are always 4 complex conjugate poles in the [sigma]-plane, symmetric only with respect to the real axis, two in the left half-plane and two in the right half-plane; therefore, the system behaviour is always oscillatory.
Checking Hurwitz-stability for [h.sub.3](A, [z.sub.1], [z.sub.2], [z.sub.3], [z.sub.4]) can be reduced to checking stability for [[??].sub.3](A, z) = [h.sub.3](A, [z.sub.1]/i, [z.sub.2]/i, [z.sub.3]/i, [z.sub.4]/i) because multiplication by the imaginary unit i maps the right half-plane to the upper half-plane.
Obviously, in this system the Nyquist loop does not encircle 1 + j0, as shown in Figure 7, because the open-loop transfer function [Y.sub.n][Z.sub.r] = (S/[r.sub.r]C)/([s.sup.2] + S/[r.sub.a]C + 1/LC) has two poles in the right half-plane and loop closing does not add any new poles.