Abstract: | The problem of robustly stabilizing an infinite dimensional system with transfer function G, subject to an additive perturbation Δ is considered. It is assumed that: G ε
0(σ) of systems introduced by Callier and Desoer 3]; the perturbation satisfies |W1ΔW2| < ε, where W1 and W2 are stable and minimum phase; and G and G + Δ have the same number of poles in
+. Now write W1GW2=G1 + G1, where G1 is rational and totally unstable and G2 is stable. Generalizing the finite dimensional results of Glover 12] this family of perturbed systems is shown to be stabilizable if and only if ε σmin (G*1)( = the smallest Hankel singular value of G*1). A finite dimensional stabilizing controller is then given by
where
2 is a rational approximation of G2 such that ) and K1 robustly stabilizes G1 to margin ε. The feedback system (G, K) will then be stable if |W1ΔW2| ∞< ε − Δ. |