On Stability Equivalence between Dynamic Output Feedback and Static Output Feedback for a Class of Second Order Infinite-Dimensional Systems

We consider stabilization for a class of abstract second order infinite-dimensional systems with collocated control and observation. We show that the closed-loop system under a proportional direct output feedback control is asymptotically stable if and only if the closed-loop system under some dynamic output feedback control is asymptotically stable. A Hautus test is developed to ensure the asymptotic stability. Two types of dynamic output feedback controls are investigated. The results are applied to some coupled wave-heat equations where the heat system is considered as a controller of the wave system. This study provides a different view in the study of the coupled systems described by partial differential equations.

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