Abstract
For an abstract free-motion system x(t) = S(t)x(0), t ≥ 0 characterized by a semigroup of linear operators S(t) on a linear space X-fundamental properties of quasiequilibrium states (QEQ) and degeneracy directions (DED) are examined. The main theorem establishes duality between these notions. The paper can be viewed as generalization of pointwise degeneracy phenomenon known for functional-differential systems and may have also considerable implications in the structure theory of infinite-dimensional input-output systems.
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