Assume that for the system of Fig. 7-1, the system closed-loop transfer-function pole p1 is repeated
such that the system characteristic equation is given by

Fig. 7-1

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(z P) (2 Pr + 1)( Pr + 2)(2 Pn) = 0 where is an integer. Show that the requirement for system stability is that the magnitudes of all poles of transfer function are less than unity, that is, the closed-loop |p| < 1, i = 1,r + 1,r + 2, ..., n.