q**Proof:** Assume g = 1. System is stable iff
det(*I-M **D*) has no zero in the closed right-half plane for all *D** *Î*RH*¥ and ||*D*||¥ £1.

(Ü ) det(*I-M **D*) ¹0 for all *D** *Î*RH*¥ and ||*D*||¥ £1 since

|l(*I-M **D*) | ³ 1-max| l(*M **D*) | ³ 1- ||*M*||¥ >0

(Þ ) Suppose ||*M*||¥ ³1. There exists a *D** *Î*RH*¥ with ||*D*||¥ £1 such that det(*I-M (s)**D**(s)*) has a zero on the imaginary axis, so the
system is unstable. Suppose *w** *Î **R**+È {¥} is such that *s*1*(M(j**w**0 **)) *³ 1. Let *M(j**w**0 **)= **U(j**w**0 **)**S**(j**w**0 **)V*(j**w**0 **) *be a singular value decomposition with

Proof