We shall construct a *D** *Î*RH*¥ such that *D**(j**w**0 **)= (1/**s*1*) v**1**u**1*** *and ||*D*||¥ £1. Indeed, for such *D**(s), *

det(*I-M (j**w**0 **)**D**(j**w**0 **)*)=det(*I- U(j**w**0 **)**S**(j**w**0 **)V(j**w**0 **) (1/**s*1*) v**1**u**1*** *)

and
thus the closed-loop system is either not well-posed (if *w**0** *= ¥) or unstable (if *w**0** *Î **R**+). There are two different cases:

(1)
*w**0** *= 0 or ¥ : Then *U* and *V* are real matrices.
Choose

(2)
0<*w**0** *< ¥ : write *u**1 *and* v**1*in the following form

where
*u**1i *,* v**1j *Î **R**
are chosen so that *q**i**, **f**j *Î [*-**p**,0*).** **

Continued.