On the transfer matrix of a neutral system: Characterizations of exponential stability in input-output terms
Two examples are presented of canonical delay systems of neutral type which show that: 1. The transfer function may be holomorphic for Re z larger than zero or on an open set which contains Re z\(>0\), even if the null solution of the free system is not exponentially stable 2. \(L^ 2\)-stability does not imply exponential stability. A final result states that some conditions are equivalent to exponential stability; in particular, the fact that the transfer function is holomorphic for Re z\(>-\sigma\), \(\sigma >0\), if the delay operator does not contain a singular part.
scientific article; zbMATH DE number 4025289
scientific article