Approximation of unstable infinite-dimensional systems using coprime factors

Abstract The effectiveness of comprime factor techniques in L 2 and L ∞ model reduction of unstable linear systems is analysed. Asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system, measured in a number of different norms, some involving the associated Hankel operators. The chordal metric is introduced as a measure of approximation and is shown to yield the graph topology. Finally it is deduced that asymptotically optimal L 2 and L ∞ convergence rates can be obtained for a large class of unstable systems.

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