Singular systems are an important class of systems from both point of view theoretical and practical. In this paper we analyze the problem of constructing feedbacks and/or output injections that suppress this disturbance in the sense that it does not affect the inputoutput behavior of the system and makes the resulting closed-loop system regular and of index at most one. All results are based on the canonical reduced forms that they can be computed using a complete system of invariants and can be implemented in a numerically stable way.

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