Stabilization in H∞R(D)
Abstract
In this paper we prove the following theorem: Suppose that f1,f2∈ H∞(), with f1∞,f2∞≤ 1, with ∈fz∈(f1(z)+f2(z))=δ>0. Assume for some ε>0 and small, f1 is positive on the set of x∈(-1,1) where f2(x)<ε for some ε>0 sufficiently small. Then there exists g1, g1-1, g2∈ H∞() with g1∞,g2∞,g1-1∞≤ C(δ,ε) and f1(z)g1(z)+f2(z)g2(z)=1∀ z∈.
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