Robust stabilization of linear multivariable systems: relations to approximation

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Abstract
The stabilization of a linear system modelled as (G + A) where G is a known rational transfer function and A is a perturbation satisfying |W,A2|∞2 is decomposed as G1 + G2 where G1 is totally unstable and G2 is stable. It is shown that there exists a single feedback controller that stabilizes (G + A) for all admissible A (that is, the robust stabilizability problem) if and only if σmin>(G1) ≥σ or equivalently there does not exist G with fewer poles in C+ than G such that |W1(G −G)W2|∞.A simple characterization of all robustly stabilizing controllers is then derived and state-space formulae for maximally robust controllers are given. Finally reduced-order controllers are considered.

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